Download App

Trigonometric Identities — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTrigonometric Identities4 Marks
Question
Prove the following identities:
$\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}+\frac{\sin\theta-\cos\theta}{\sin\theta+\cos\theta}=\frac{2}{\big(1-2\cos^2\theta\big)}$
✓

Answer

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

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

Find the distance between of the following points from the origin:
$C(-4, -6)$
→
Find the values of a and b for which the following system of equations has infinitely many solutions:
$2x + 3y = 7$
$(a - 1)x + (a + 2)y = 3a$
→
Solve for $x$ and $y:$
$\frac{10}{\text{x}+\text{y}}+\frac{2}{\text{x}-\text{y}}=4,$
$\frac{15}{\text{x}+\text{y}}-\frac{9}{\text{x}-\text{y}}=-2$
→
If $\cot\theta=2,$ find the value of the all $T$-ratios of $\theta.$
→
Find the sum of all natural numbers between $200$ and $400$ which are divisible by $7.$
→
Prove the following identities:
$\text{cosec}^4\theta-\text{cosec}^2\theta=\cot^4\theta+\cot^2\theta$
→
Find the lenght of a diagonal of a rectangle whose adjacent side are $30\ cm$ and $16\ cm.$
→
Some students planned a picnic. The budget for food was Rs. $480$. But eight of these failed to go and thus the cost of food for each member increased by Rs. $10$. How many students attended the picnic?
→
Prove that the points $(3, -2), (4, 0), (6, -3)$ and $(5, -5)$ are the vertices of a parallelogram.
→
Using Euclid’s division algorithm, find the largest number that divides $1251, 9377$ and $15628$ leaving remainders $1, 2$ and $3$ respectively.
→