Question
Prove that: $\cos ^{-1} \frac{12}{13}+\sin ^{-1} \frac{4}{5}=\tan ^{-1} \frac{63}{16}$

Answer

self

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

Similar questions

Write a value of $\int\frac{1}{1+\text{e}^{\text{x}}}\text{dx}$
Solve the Linear Programming Problem graphically:
Minimize Z = -3x + 4y subject to $x + 2y \leq 8, \ 3x + 2y \leq 12, \ x \geq 0, \ y \geq 0.$
Find the angle between two lines, one of which has direction ratios 2, 2, 1 while the other one is obtained by joining the points (3, 1, 4) and (7, 2, 12).
If $\text{y}=\text{e}^\text{x}\cos\text{x},$ prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{e}^\text{x}\cos(\text{x}+\frac{\pi}{2}).$
Determine the value of the constant k so that the function
$\text{f}\text{(x)}=\begin{cases}\frac{\text{x}^2-3\text{x}+2}{\text{x}-1}, &\text{if}\text{ x}\neq1\\\text{k}, &\text{if}\text{ x}=1\end{cases}$ is continuous at x = 1
Find $\int \frac{x^2-3 x+1}{\sqrt{1-x^2}} d x$
Find the angle between the given planes.
$\vec{\text{r}}\cdot(2\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}})=1$ and $\vec{\text{r}}\cdot(-\hat{\text{i}}+\hat{\text{j}})=4$
Find a vector whose length is 3 and which is perpendicular to the vector $\vec{\text{a}}=3\hat{\text{i}}+\hat{\text{j}}-4\hat{\text{k}}$ and $\vec{\text{b}}=6\hat{\text{i}}+5\hat{\text{j}}-2\hat{\text{k}}.$
For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
$\text{y}=\text{x}\sin​3\text{x}​$ : $\frac{\text{d}^2\text{y}}{\text{dx}^2}+9\text{y}-6\cos3\text{x}=0$
Find the points o local maxima or local minima, if any, of the following functions, using the first derivatives test. Also, find the local maximum or local minimum values, as the case may be:
$\text{f}(\text{x})=\text{x}^{3}-6\text{x}^{2}+9\text{x}+15$