Evaluate: ^ -1 (-3 5 )+ ^ -1 (-5 12 ) - Vidyadip

Question

Evaluate: $\sin\Big\{\cos^{-1}\Big(-\frac{3}{5}\Big)+\cot^{-1}\Big(-\frac{5}{12}\Big)\Big\}$

✓

Answer

$\sin\Big\{\cos^{-1}\Big(-\frac{3}{5}\Big)+\cot^{-1}\Big(-\frac{5}{12}\Big)\Big\}$
$=\sin\Big\{\pi-\cos^{-1}\Big(\frac{3}{5}\Big)+\pi-\cot^{-1}\Big(\frac{5}{12}\Big)\Big\}$
$=\sin\Big\{2\pi-\Big[\cos^{-1}\Big(\frac{3}{5}\Big)+\cot^{-1}\Big(\frac{5}{12}\Big)\Big]\Big\}$
$=-\sin\Big\{\cos^{-1}\Big(\frac{3}{5}\Big)+\cot^{-1}\Big(\frac{5}{12}\Big)\Big\}$
$=-\sin\begin{Bmatrix}\sin^{-1}\Bigg[\sqrt{1-\Big(\frac{3}{5}\Big)^2}\Bigg]=\sin^{-1}\begin{bmatrix}\frac{\frac{12}{5}}{\sqrt{1+\big(\frac{12}{5}\big)^2}}\end{bmatrix}\end{Bmatrix}$
$=-\sin\Big(\sin^{-1}\frac{4}{5}+\sin^{-1}\frac{12}{13}\Big)$
$=-\sin\Bigg\{\sin^{-1}\Bigg[\frac{4}{5}\times\sqrt{1-\Big(\frac{12}{13}\Big)^2}+\frac{12}{13}\times\sqrt{1-\Big(\frac{4}{5}\Big)^2}\Bigg]\Bigg\}$
$=-\sin\Big[\sin^{-1}\Big(\frac{20}{65}+\frac{36}{64}\Big)\Big]$
$=-\sin\Big[\sin^{-1}\Big(\frac{56}{65}\Big)\Big]$
$=-\frac{56}{65}$

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 "Solve the Following Question.(5 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the points on the curve $x^2 + y^2 - 2x - 3 = 0$ at which the tangents are parallel to the x-axis.

Find the distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z.

Prove the following identities:
$\begin{vmatrix}\text{y}+\text{z}&\text{z}&\text{y}\\\text{z}&\text{z}+\text{x}&\text{x}\\\text{y}&\text{x}&\text{x}+\text{y}\end{vmatrix}=4\text{xyz}$

Verify Rolle's theorem of the following function on the indicated interval
$\text{f}(\text{x})=2\sin\text{x}+\sin2\text{x}\text{ on }[0,\pi]$

m is said to be related to n if m and n are integers and m - n is divisible by 13. Does this define an equivalence relation?

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = (x - 1)(x - 2)^2$

A firm manufactures two types of products $A$ and $B$ and sells them at a profit of $R s 2$ on type $A$ and $R s 3$ on type $B$. Each product is processed on two machines $M_1$ and $M_2$. Type $A$ requires one minute of processing time on $M_1$ and two minutes of $M _2$; type $B$ requires one minute on $M _1$ and one minute on $M _2$. The machine $M _1$ is available for not more than 6 hours 40 minutes while machine $M _2$ is available for 10 hours during any working day. Formulate the problem as a LPP.

Find $\frac{\text{dy}}{\text{dx}}$
$\text{y}=\text{x}^{\cos\text{x}}+(\sin\text{x})^{\tan\text{x}}$

Find the inverse of the following matrices by using elementry row transformation:$\begin{bmatrix}2 & 5 \\ 1 & 3 \end{bmatrix}$

Solve the following differential equation:
$\text{y e}^{\frac{\text{x}}{\text{y}}}\text{dx}=\big(\text{xe}^{\frac{\text{x}}{\text{y}}}+\text{y}\big)\text{dy}$