The value of tan^ -1 (sin2 -1 cos2 ) is equal to:- - Vidyadip

MCQ

The value of $tan^{-1} (\frac{sin2 -1}{cos2})$ is equal to:-

A
$\frac{\pi}{2} - 1$
B
$2 - \frac{\pi}{2}$
✓
$1- \frac{\pi}{4}$
D
$ \frac{\pi}{4}-1$

✓

Answer

Correct option: C.

$1- \frac{\pi}{4}$

c
$\tan ^{-1}\left[\frac{2 \sin 1 \cos 1-\cos ^{2} 1-\sin ^{2} 1}{\cos ^{2} 1-\sin ^{2} 1}\right]$

$=-\tan ^{-1} \frac{\cos 1-\sin 1}{\cos 1+\sin 1}$

$=-\tan ^{-1} \tan \left[\frac{\pi}{4}-1\right]$

$=1-\frac{\pi}{4}$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $A$ and $B$ be subsets of a set $X$. Then

If the function $f(x)=\frac{\cos (\sin x)-\cos x}{x^{4}}$ is continuous at each point in its domain and $f (0)=\frac{1}{ k },$ then $k$ is ........

If $\mathop {\lim }\limits_{x \to \infty } {\left( {\frac{{{a^{1/x}} + b}}{c}} \right)^x} = d$ (non zero finite), then $(b + 1)log_a\,d$ is

If $\int_2^e {\left[ {\frac{1}{{\log x}} - \frac{1}{{{{(\log x)}^2}}}} \right]} \,dx = \alpha + \frac{\beta }{{\log 2}},$ then

If $y = {(1 + x)^x},$ then ${{dy} \over {dx}} = $

If $n (2 n +1) \int_{0}^{1}\left(1- x ^{ n }\right)^{2 n } dx =1177 \int_{0}^{1}\left(1- x ^{ n }\right)^{2 n +1} dx$, then $n \in N$ is equal to $\dots\dots$

Give the number of common tangents to circle ${x^2} + {y^2} + 2x + 8y - 23 = 0$ and ${x^2} + {y^2} - 4x - 10y + 9 = 0$

The number of real roots of the equation $x | x |-5| x +2|+6=0$, is

If $\left| {\,\begin{array}{*{20}{c}}1&k&3\\3&k&{ - 2}\\2&3&{ - 1}\end{array}\,} \right| = 0$,then the value of $ k $ is

If the coordinates of the vertices $ A, B, C$ of the triangle $ABC$ be $( - \;4,\;2),$ $(12,\; - 2)$ and $(8,\;6)$ respectively, then $\angle \;B$=