Question 12 Marks
Without using trigonometric tables, evaluate.
$\cos ^2 24+\cos ^2 66$
View full question & answer→Question 22 Marks
Without using trigonometric tables, evaluate.
$\operatorname{cosec}^2 48-\tan ^2 52$
View full question & answer→Question 32 Marks
Without using trigonometric tables, evaluate.
$\sec ^2 36-\cot ^2 54$
View full question & answer→Question 42 Marks
Without using trigonometric tables, evaluate.
$\sin ^2 23+\sin ^2 67$
View full question & answer→Question 52 Marks
Without using trigonometric tables, evaluate.
$\cos ^2 25-\sin ^2 65$
View full question & answer→Question 62 Marks
Without using trigonometric tables, evaluate.
$\sin 37-\cos 53$
View full question & answer→Question 72 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 28^{\circ} 54^{\prime}}{\sec 61^{\circ} 6^{\prime}}+\frac{\cos 28^{\circ} 54^{\prime}}{\operatorname{cosec} 61^{\circ} 6^{\prime}}$
Answer1
$\left[\right.$ Hint . Given exp. $\left.\frac{\sin 29^{\circ} 31^{\prime}}{\cos \left[90^{\circ}-\left(29^{\circ} 31^{\prime}\right)\right.}\right]$.
View full question & answer→Question 82 Marks
Without using trigonometric tables, evaluate.
$\frac{\tan 20^{\circ} 43^{\prime}}{\cot 69^{\circ} 17^{\prime}}$
Answer1
$\left[\right.$ Hint . Given exp. $\left.\frac{\sin 29^{\circ} 31^{\prime}}{\cos \left[90^{\circ}-\left(29^{\circ} 31^{\prime}\right)\right.}\right]$.
View full question & answer→Question 92 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 29^{\circ} 31^{\prime}}{\cos 60^{\circ} 29^{\prime}}$
Answer1
$\left[\right.$ Hint . Given exp. $\left.\frac{\sin 29^{\circ} 31^{\prime}}{\cos \left[90^{\circ}-\left(29^{\circ} 31^{\prime}\right)\right.}\right]$.
View full question & answer→Question 102 Marks
Without using trigonometric tables, evaluate.
$4 \tan 60 \sec 30+\frac{\sin 31^{\circ} \sec 59^{\circ}+\cot 59^{\circ} \cot 31^{\circ}}{8 \sin ^2 30^{\circ}-\tan ^2 45^{\circ}}$
Answer10
\[\left[\text { Hint . Given exp. }=\frac{\sin (90-55) \cos 55+\cos (90-55) \sin 55}{\operatorname{cosec}^2(90-80)^2-\tan ^2 80}\right] .\]
View full question & answer→Question 112 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 35^{\circ} \cos 55^{\circ}+\cos 35^{\circ} \sin 55^{\circ}}{\operatorname{cosec}^2 10^{\circ}-\tan ^2 80^{\circ}}$
Answer1
\[\left[\text { Hint . Given exp. }=\frac{\sin (90-55) \cos 55+\cos (90-55) \sin 55}{\operatorname{cosec}^2(90-80)^2-\tan ^2 80}\right] .\]
View full question & answer→Question 122 Marks
Without using trigonometric tables, evaluate.
$5 \sin 70 \sec 20-3 \sin 50 \sec 40$
View full question & answer→Question 132 Marks
Without using trigonometric tables, evaluate.
$3 \cos 80 \operatorname{cosec} 10+2 \cos 59 \operatorname{cosec} 31$
View full question & answer→Question 142 Marks
Without using trigonometric tables, evaluate.
$\left(\frac{\operatorname{cosec} 34^{\circ}}{\sec 56^{\circ}}\right)^2+\left(\frac{\cot 81^{\circ}}{\tan 9^{\circ}}\right)^2$
View full question & answer→Question 152 Marks
Without using trigonometric tables, evaluate.
$\left(\frac{\sin 39^{\circ}}{\cos 51^{\circ}}\right)^2+\left(\frac{\cos 51^{\circ}}{\sin 39^{\circ}}\right)^2$
View full question & answer→Question 162 Marks
Without using trigonometric tables, evaluate.
$\frac{\cos 35^{\circ}}{\sin 55^{\circ}}+\frac{\sin 11^{\circ}}{\cos 79^{\circ}}-\cos 28^{\circ} \operatorname{cosec} 62^{\circ}$
View full question & answer→Question 172 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 80^{\circ}}{\cos 10^{\circ}}+\sin 59^{\circ} \sec 31^{\circ}$
View full question & answer→Question 182 Marks
Without using trigonometric tables, evaluate.
$\frac{2 \tan 53^{\circ}}{\cot 37^{\circ}}-\frac{\cot 80^{\circ}}{\tan 10^{\circ}}$
View full question & answer→Question 192 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 72^{\circ}}{\cos 18^{\circ}}-\frac{\sec 32^{\circ}}{\operatorname{coses} 58^{\circ}}$
View full question & answer→Question 202 Marks
Without using trigonometric tables, evaluate.
$\frac{\tan 19^{\circ}}{\cot 71^{\circ}}$
View full question & answer→Question 212 Marks
Without using trigonometric tables, evaluate.
$\frac{\sec 38^{\circ}}{\operatorname{cosec} 52^{\circ}}$
View full question & answer→Question 222 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 27^{\circ}}{\cos 63^{\circ}}$
View full question & answer→Question 232 Marks
Without using trigonometric tables, evaluate.
$\frac{\operatorname{cosec}^2 67^{\circ}-\tan ^2 23^{\circ}}{\sec ^2 20^{\circ}-\cot ^2 70^{\circ}}$
View full question & answer→Question 242 Marks
Without using trigonometric tables, evaluate.
$\frac{\cos ^2 34^{\circ}+\cos ^2 56^{\circ}}{\sin ^2 59^{\circ}+\sin ^2 31^{\circ}}$
View full question & answer→Question 252 Marks
If $A=45$, verify that :
$\cos 2 A=\left(2 \cos ^2 A-1\right)=\left(1-2 \sin ^2 A\right)$
View full question & answer→Question 262 Marks
If $A=45$, verify that :
$\sin 2 A=2 \sin A \cos A$
View full question & answer→Question 272 Marks
Verify the following : $2 \sin 45 \cos 45=\sin 90$.
View full question & answer→Question 282 Marks
Verify the following : $2 \sin 30 \cos 30=\sin 60$.
View full question & answer→Question 292 Marks
Verify the following : $\sin 60 \cos 30-\cos 60 \sin 30=\sin 30$.
View full question & answer→Question 302 Marks
Verify the following : $\tan 30^{\circ}=\left(\frac{\tan 60^{\circ}-\tan 30^{\circ}}{1+\tan 60^{\circ} \tan 30^{\circ}}\right)$.
View full question & answer→Question 312 Marks
Verify the following : $\cos 60=\left(1-2 \sin ^2 30\right)=\left(2 \cos ^2 30-1\right)$.
View full question & answer→Question 322 Marks
Verify the following : $\cos 60 \cos 30-\sin 60 \sin 30=0$.
View full question & answer→Question 332 Marks
Without using trigonometric tables, find the values of :
$4\left(\sin ^4 30+\cos ^4 60\right)-3\left(\cos ^2 45-\sin ^2 90\right)$.
View full question & answer→Question 342 Marks
Without using trigonometric tables, find the values of :
$\frac{\tan ^2 60^{\circ}+4 \cos ^2 45^{\circ}+\sec ^2 30^{\circ}+5 \cos ^2 90^{\circ}}{\operatorname{cosec} 30^{\circ}+\sec 60^{\circ}-\cot ^2 30^{\circ}}$
View full question & answer→Question 352 Marks
Without using trigonometric tables, find the values of :
$\frac{5 \sin ^2 30^{\circ}+\cos ^2 45^{\circ}-4 \tan ^2 30^{\circ}}{2 \sin 30^{\circ} \cos 30^{\circ}+\tan 45^{\circ}}$
Answer$\frac{5}{6(2+\sqrt{3})}$
View full question & answer→Question 362 Marks
Without using trigonometric tables, find the values of :
$\frac{\sin 30^{\circ}-\sin 90^{\circ}+2 \cos 0^{\circ}}{\tan 30^{\circ} \times \tan 60^{\circ}}$
View full question & answer→Question 372 Marks
Without using trigonometric tables, find the values of :
$\frac{\sin ^2 45^{\circ}+\cos ^2 45^{\circ}}{\tan ^2 60^{\circ}}$
View full question & answer→Question 382 Marks
Without using trigonometric tables, find the values of :
$\frac{4}{3} \tan ^2 30+\sin ^2 60-3 \cos ^2 60+\frac{3}{4} \tan ^2 60-2 \tan ^2 45$.
View full question & answer→Question 392 Marks
Without using trigonometric tables, find the values of :
$2 \sqrt{2} \cos 45 \cos 60+2 \sqrt{3} \sin 30 \tan 60-\cos 0$
View full question & answer→Question 402 Marks
Without using trigonometric tables, find the values of :
$(\cos 0+\sin 45+\sin 30)(\sin 90-\cos 45+\cos 60)$
View full question & answer→Question 412 Marks
Without using trigonometric tables, find the values of :
$\left(3 \cos ^2 30+\tan ^2 60\right)$
View full question & answer→Question 422 Marks
Without using trigonometric tables, find the value of :
$\left(3 \sin ^2 45+2 \cos ^2 60\right)$
View full question & answer→Question 432 Marks
Without using trigonometric tables, find the values of :
$\cos 90+\cos ^2 45 \sin 30 \tan 45$
View full question & answer→Question 442 Marks
Without using trigonometric tables, find the values of :
$\cos 60 \cos 45+\sin 60 \sin 45$
Answer$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
View full question & answer→Question 452 Marks
Without using trigonometric tables, find the values of :
$\sin 45 \cos 30-\cos 45 \sin 30$
Answer$\frac{\sqrt{3}-1}{2 \sqrt{2}}$
View full question & answer→Question 462 Marks
Without using trigonometric tables, find the values of :
$\sin 60 \cos 30+\cos 60 \sin 30$
View full question & answer→Question 472 Marks
If $0^{\circ} \leq x \leq 90^{\circ}$, state the numerical value of $x$ for which $\sin x=\cos x$.
View full question & answer→Question 482 Marks
Without using tables, verify that : $\cos 60=\frac{1-\tan ^2 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{1}{2}$.
View full question & answer→Question 492 Marks
Without using tables, verify that : $\sin 60=\frac{2 \tan 30^{\circ}}{1+\tan ^2 30^{\circ}}=\frac{\sqrt{3}}{2}$.
View full question & answer→Question 502 Marks
Without using tables, verify that : $\cos 60=\left(\cos ^2 30-\sin ^2 30\right)$.
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