sin ^{-1}(sin 100) + cos ^{-1}(cos 100) + tan | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We know the principal value ranges: $\sin^{-1}(\sin x) = x - n\pi$ or $(n+1)\pi - x$,$\cos^{-1}(\cos x) = |x - 2n\pi|$,$	an^{-1}(	an x) = x - n\

Vedclass · Accepted Answer

$200 - 63\pi$

Vedclass · Answer

(C) We know the principal value ranges: $\sin^{-1}(\sin x) = x - n\pi$ or $(n+1)\pi - x$,$\cos^{-1}(\cos x) = |x - 2n\pi|$,$	an^{-1}(	an x) = x - n\pi$,and $\cot^{-1}(\cot x) = x - n\pi$.
For $x = 100$,we note that $31\pi \approx 97.389$ and $32\pi \approx 100.53$.
Since $31\pi < 100 < 32\pi$:
$1$. $\sin^{-1}(\sin 100) = 100 - 32\pi$ (as $100$ is in the range where $\sin x$ is negative and decreasing).
$2$. $\cos^{-1}(\cos 100) = 32\pi - 100$ (since $100$ is in the interval $(31\pi, 32\pi)$).
$3$. $	an^{-1}(	an 100) = 100 - 32\pi$ (since $100$ is in the interval $(31\pi, 32\pi)$).
$4$. $\cot^{-1}(\cot 100) = 100 - 31\pi$ (since $100$ is in the interval $(31\pi, 32\pi)$).
Summing these: $(100 - 32\pi) + (32\pi - 100) + (100 - 32\pi) + (100 - 31\pi) = 200 - 63\pi$.

$\sin ^{-1}(\sin 100) + \cos ^{-1}(\cos 100) + \tan ^{-1}(\tan 100) + \cot ^{-1}(\cot 100)$ equals to:

Similar Questions

The value of $\lim_{x \to 1/\sqrt{2}} \frac{x - \cos(\sin^{-1} x)}{1 - \tan(\sin^{-1} x)}$ is

If $y = \sum_{k=1}^{6} k \cos^{-1} \left\{ \frac{3}{5} \cos kx - \frac{4}{5} \sin kx \right\}$,then $\frac{dy}{dx}$ at $x = 0$ is

Let $\cos ^{-1}(x) + \cos ^{-1} (2x) + \cos ^{-1}(3x) = \pi.$ If $x$ satisfies the cubic equation $ax^3 + bx^2 + cx - 1 = 0,$ then the value of $(a + b + c)$ is -

Which pair$(s)$ of function$(s)$ is/are equal? (where ${x}$ and $[x]$ denote the fractional part and integral part functions respectively.)

If $a, b, c$ are positive real numbers and the value of $\theta = \tan^{-1}\sqrt{\frac{a(a+b+c)}{bc}} + \tan^{-1}\sqrt{\frac{b(a+b+c)}{ca}} + \tan^{-1}\sqrt{\frac{c(a+b+c)}{ab}}$,then $\tan \theta$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module