Download App

Trigonometric Identities — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTrigonometric Identities4 Marks
Question
Prove the following identities:
$\frac{(\sin\text{A}-\sin\text{B})}{(\cos\text{A}+\cos\text{B})}+\frac{(\cos\text{A}-\cos\text{B})}{(\sin\text{A}+\sin\text{B})}=0$
✓

Answer

$\text{LHS}=\frac{(\sin\text{A}-\sin\text{B})}{(\cos\text{A}+\cos\text{B})}+\frac{(\cos\text{A}-\cos\text{B})}{(\sin\text{A}+\sin\text{B})}$
$=\frac{(\sin\text{A}+\sin\text{B})(\sin\text{A}-\sin\text{B})+(\cos\text{A}+\cos\text{B})(\cos\text{A}-\cos\text{B})}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=\frac{\sin^2\text{A}-\sin^2\text{B}+\cos^2\text{A}-\cos^2\text{B}}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=\frac{\big(\sin^2\text{A}+\cos^2\text{A}\big)-\big(\sin^2\text{A}+\cos^2\text{B}\big)}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=\frac{1-1}{(\cos\text{A}+\cos\text{B})(\sin\text{A}+\sin\text{B})}$
$=0$
$=\text{R.H.S}$
$\therefore\ \text{L.H.S.}=\text{R.H.S.}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Trigonometric Identities→Trigonometric Identities — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Solve the following system of equations by the method of cross-multiplication:
$x + ay = b,$
$ax - by = c.$
→
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^2- 3x - 2,$ find a quadratic polynomial whose zeroes are $\frac{1}{2\alpha+\beta}$ and $\frac{1}{2\beta+\alpha}.$
→
Solve the following quadratic equations by factorization:
$\frac{3}{\text{x}+1}-\frac{1}{2}=\frac{2}{3\text{x}-1},$ $\text{x}\neq-1,\frac{1}{3}$
→
The angle of elevation of the top of a tower as observed form a point in a horizontal plane through the foot of the tower is $32^\circ $. When the observer moves towards the tower a distance of $100\ m$, he finds the angle of elevation of the top to be $63^\circ $. Find the height of the tower and the distance of the first position from the tower. [Take $\tan32^\circ = 0.6248$ and $\tan 63^\circ = 1.9626]$
→
Two concentric circles are of radii $5\ cm$ and $3\ cm.$ Find the length of the chord of the larger circle which touches the smaller circle.
→
Find the area of the major segment $APB$ of a circle of radius 35cm and $\angle\text{AOB}=90^\circ$ as shown in the given figure.
→
Six bells commence tolling together and toll at intervals of $2, 4, 6, 8, 10, 12$ minutes respectively. In $30$ hours, how many times do they toll together?
→
Prove the following identities:
$\frac{\tan\theta}{(1-\cot\theta)}+\frac{\cot\theta}{(1-\tan\theta)}=(1+\sec\theta\text{ cosec }\theta)$
→
A tower subtends an angle $\alpha$ at a point A in the plane of its base and the angles of depression of the foot of the tower at a point b metres just above A is $\beta.$ Prove that the height of the tower is $\text{b}\tan\alpha\cot\beta.$
→
A two-digit number is $4$ times the sum of its digits. If $18$ is added to the number, the digits are reversed. Find the number.
→