Prove that ^ –1 (8 17 )+ ^ -1 (3 5 )= ^ -1 (36 85 ). - Vidyadip

Question

Prove that $\sin^{–1} \Bigg(\frac{8}{17}\Bigg)+\sin^{-1}\Bigg(\frac{3}{5}\Bigg)=\cos^{-1}\Bigg(\frac{36}{85}\Bigg).$

✓

Answer

Writing $\sin^{-1 }\Bigg(\frac{18}{17}\Bigg)=\tan^{-1}\frac{8}{15}$ and $\sin^{-1 }\Bigg(\frac{3}{5}\Bigg)=\tan^{-1}\frac{3}{4}$
$\therefore LHS = \tan^{-1 }\frac{8}{15}+\tan^{-1}\frac{3}{4}=\tan^{-1}\Bigg(\frac{\frac{8}{15}+\frac{3}{4}}{1-\frac{8}{15}\cdot\frac{3}{4}}\Bigg)=\tan^{1}\Bigg(\frac{77}{36}\Bigg)$
Getting $\tan^{–1 }\Bigg(\frac{77}{36}\Bigg)=\cos^{-1}\Bigg(\frac{36}{85}\Bigg).$

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 "3 Marks Question" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let S be the set of all rational numbers of the for $\frac{\text{m}}{\text{n}},$ where $\text{m}\in\text{Z}$ and n = 1, 2, 3. Prove that * on sdefined by a * b = ab is not a binary operation.

If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?

Evaluate the following integrals:$\int\frac{1}{\text{x}^{\frac{2}{3}}\sqrt{\text{x}^{\frac{2}{3}}-4}}\text{ dx}$

Find the inverse of $5$ under multiplication modulo $11$ on $Z_{11}.$

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\text{|x|}\cos\Big(\frac{1}{\text{x}}\Big), & \text{ x}\neq 0\\0 &\text{ x} = 0\end{cases}\text{at x}=0$

Show that the logarithmic function $\text{f}:\text{R}0^+\rightarrow \text{R}$ given by $f(x) = log_a x, a > 0$ is a bijection.

Evaluate the integral: $\sec ^{-1} \sqrt{x} d x$

Represent the following families of curves by forming the corresponding differential equation:
$\text{y}=4\text{ax}$

Differentiate the function $x^{x}-2^{\sin x} w.r.t. x.$

Differentiate the function $sin ^{-1}({x\sqrt x})\ ,{0 \leq x \leq 1}$ w.r.t. to x.