Question 512 Marks
Show that $4\left(\sin ^4 30+\cos ^4 60\right)-3\left(\cos ^2 45-\sin ^2 90\right)=2$.
View full question & answer→Question 522 Marks
If $\tan \theta=\frac{5}{12}$ and $\theta$ is acute, find the values of $\sin \theta$ and $\cos \theta$.
Answer$\sin \theta=\frac{5}{13}, \cos \theta=\frac{12}{13}$
View full question & answer→Question 532 Marks
If $\sin \theta=\frac{3}{5}$ and $\theta$ is an acute angle, find the values of $\cos \theta$ and $\tan \theta$.
Answer$\cos \theta=\frac{4}{5}, \tan \theta=\frac{3}{4}$
View full question & answer→Question 542 Marks
If $(\cos \theta+\sec \theta)=\frac{5}{2}$, find the value of $\left(\cos ^2 \theta+\sec ^2 \theta\right)$.
View full question & answer→Question 552 Marks
If $(\tan \theta+\cot \theta)=5$, find the value of $\left(\tan ^2 \theta+\cot ^2 \theta\right)$.
View full question & answer→Question 562 Marks
If $13 \sin \theta=5$, find the value of $\frac{(5 \sin \theta-2 \cos \theta)}{\tan \theta}$.
View full question & answer→Question 572 Marks
If $\sin \theta=\frac{\sqrt{3}}{2}$, find the value of $(\operatorname{cosec} \theta+\cot \theta)$.
View full question & answer→Question 582 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 592 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 602 Marks
Without using trigonometric tables, evaluate.
$\cos ^2 24^{\circ}+\cos ^2 66^{\circ}$
View full question & answer→Question 612 Marks
Without using trigonometric tables, evaluate.
$\operatorname{cosec}^2 48^{\circ}-\tan ^2 52^{\circ}$
View full question & answer→Question 622 Marks
Without using trigonometric tables, evaluate.
$\sec ^2 36^{\circ}-\cot ^2 54^{\circ}$
View full question & answer→Question 632 Marks
Without using trigonometric tables, evaluate.
$\sin ^2 23^{\circ}+\sin ^2 67^{\circ}$
View full question & answer→Question 642 Marks
Without using trigonometric tables, evaluate.
$\cos ^2 25^{\circ}-\sin ^2 65^{\circ}$
View full question & answer→Question 652 Marks
Without using trigonometric tables, evaluate.
$\sin 37^{\circ}-\cos 53^{\circ}$
View full question & answer→Question 662 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 28^{\circ} 54^{\prime}}{\sec 61^{\circ} 6^{\prime}}+\frac{\cos 28^{\circ} 54^{\prime}}{\operatorname{cosec} 61^{\circ} 6^{\prime}}$
View full question & answer→Question 672 Marks
Without using trigonometric tables, evaluate.
$\frac{\tan 20^{\circ} 43^{\prime}}{\cot 69^{\circ} 17^{\prime}}$
View full question & answer→Question 682 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 29^{\circ} 31^{\prime}}{\cos 60^{\circ} 29^{\prime}}$
$\left[\right.$ Hint. Given $\left.\exp. \frac{\sin 29^{\circ} 31^{\prime}}{\cos \left[90^{\circ}-\left(29^{\circ} 31^{\prime}\right)\right.}\right]$.
View full question & answer→Question 692 Marks
Without using trigonometric tables, evaluate.
$4 \tan 60^{\circ} \sec 30^{\circ}+\frac{\sin 31^{\circ} \sec 59^{\circ}+\cot 59^{\circ} \cot 31^{\circ}}{8 \sin ^2 30^{\circ}-\tan ^2 45^{\circ}}$
$\left[\right.$ Hint . Given exp. $\left.=\frac{\sin \left(90^{\circ}-55^{\circ}\right) \cos 55^{\circ}+\cos \left(90^{\circ}-55^{\circ}\right) \sin 55^{\circ}}{\operatorname{cosec}^2\left(90^{\circ}-80^{\circ}\right)^2-\tan ^2 80^{\circ}}\right]$
View full question & answer→Question 702 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 35^{\circ} \cos 55^{\circ}+\cos 35^{\circ} \sin 55^{\circ}}{\operatorname{cosec}^2 10^{\circ}-\tan ^2 80^{\circ}}$
View full question & answer→Question 712 Marks
Without using trigonometric tables, evaluate.
$5 \sin 70^{\circ} \sec 20^{\circ}-3 \sin 50^{\circ} \sec 40^{\circ}$
View full question & answer→Question 722 Marks
Without using trigonometric tables, evaluate.
$3 \cos 80^{\circ} \operatorname{cosec} 10^{\circ}+2 \cos 59^{\circ} \operatorname{cosec} 31^{\circ}$
View full question & answer→Question 732 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 742 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 752 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 762 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 80^{\circ}}{\cos 10^{\circ}}+\sin 59^{\circ} \sec 31^{\circ}$
View full question & answer→Question 772 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 782 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 792 Marks
Without using trigonometric tables, evaluate.
$\frac{\tan 19^{\circ}}{\cot 71^{\circ}}$
View full question & answer→Question 802 Marks
Without using trigonometric tables, evaluate.
$\frac{\sec 38^{\circ}}{\operatorname{cosec} 52^{\circ}}$
View full question & answer→Question 812 Marks
Without using trigonometric tables, evaluate.
$\frac{\sin 27^{\circ}}{\cos 63^{\circ}}$
View full question & answer→Question 822 Marks
Verify the following:
$2 \sin 45^{\circ} \cos 45^{\circ}=\sin 90^{\circ}$
View full question & answer→Question 832 Marks
Verify the following:
$2 \sin 30^{\circ} \cos 30^{\circ}=\sin 60^{\circ}$.
View full question & answer→Question 842 Marks
Verify the following:
$\sin 60^{\circ} \cos 30^{\circ}-\cos 60^{\circ} \sin 30^{\circ}=\sin 30^{\circ}$.
View full question & answer→Question 852 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 862 Marks
Verify the following:
$\cos 60^{\circ}=\left(1-2 \sin ^2 30^{\circ}\right)=\left(2 \cos ^2 30^{\circ}-1\right)$.
View full question & answer→Question 872 Marks
Verify the following:
$\cos 60^{\circ} \cos 30^{\circ}-\sin 60^{\circ} \sin 30^{\circ}=0$.
View full question & answer→Question 882 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 892 Marks
Without using trigonometric tables, find the values of:
$\frac{4}{3} \tan ^2 30^{\circ}+\sin ^2 60^{\circ}-3 \cos ^2 60^{\circ}+\frac{3}{4} \tan ^2 60^{\circ}-2 \tan ^2 45^{\circ}$
View full question & answer→Question 902 Marks
Without using trigonometric tables, find the values of:
$2 \sqrt{2} \cos 45^{\circ} \cos 60^{\circ}+2 \sqrt{3} \sin 30^{\circ} \tan 60^{\circ}-\cos 0^{\circ}$
View full question & answer→Question 912 Marks
Without using trigonometric tables, find the values of:
$\left(\cos 0^{\circ}+\sin 45^{\circ}+\sin 30^{\circ}\right)\left(\sin 90^{\circ}-\cos 45^{\circ}+\cos 60^{\circ}\right)$
View full question & answer→Question 922 Marks
Without using trigonometric tables, find the values of:
$\left(3 \cos ^2 30^{\circ}+\tan ^2 60^{\circ}\right)$
View full question & answer→Question 932 Marks
Without using trigonometric tables, find the values of:
$\left(3 \sin ^2 45^{\circ}+2 \cos ^2 60^{\circ}\right)$
View full question & answer→Question 942 Marks
Without using trigonometric tables, find the values of:
$\cos 90^{\circ}+\cos ^2 45^{\circ} \sin 30^{\circ} \tan 45^{\circ}$
View full question & answer→Question 952 Marks
Without using trigonometric tables, find the values of:
$\cos 60^{\circ} \cos 45^{\circ}+\sin 60^{\circ} \sin 45^{\circ}$
Answer$\frac{\sqrt{3}+1}{2 \sqrt{2}}$
View full question & answer→Question 962 Marks
Without using trigonometric tables, find the values of:
$\sin 45^{\circ} \cos 30^{\circ}-\cos 45^{\circ} \sin 30^{\circ}$
Answer$\frac{\sqrt{3}-1}{2 \sqrt{2}}$
View full question & answer→Question 972 Marks
Without using trigonometric tables, find the values of:
$\sin 60^{\circ} \cos 30^{\circ}+\cos 60^{\circ} \sin 30^{\circ}$
View full question & answer→