Question
Evaluate the following:
$\tan^{-1}(\tan1)$
$\tan^{-1}(\tan1)$
✓
Answer
We know that $\tan^{-1}(\tan\theta)=\theta,-\frac{\pi}{2}<\theta<\frac{\pi}{2}$$\tan^{-1}(\tan1)$
$=1$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta,\text{if }\theta\in\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big)\Big)$
$=1$ $\Big(\because\ \tan^{-1}(\tan\theta)=\theta,\text{if }\theta\in\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big)\Big)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the distance between the planes $2x – y + 2z = 5$ and $5x – 2.5y + 5z = 20$.
→Evaluate the following:
$\sec^{-1}\Big(\sec\frac{\pi}{3}\Big)$
→$\sec^{-1}\Big(\sec\frac{\pi}{3}\Big)$
Sand is pouring from a pipe at the rate of $12cm^3/s$. the falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is $4 cm$?
→Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find: P(neither A nor B)
Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find:
5 * 7, 20 * 16
5 * 7, 20 * 16
Find the value of $\cos^{-1}\Big(\cos\frac{13\pi}{6}\Big)$
→ In Fig 10.6 (a square), identify the following vectors.
Collinear but not equal.
Collinear but not equal.
Evaluate $\int_{0}^{\frac{\pi}{4}} \sin ^{3} 2 t \cos 2 t d t$
→$\int \frac{d x}{\sin ^{2} x \cos ^{2} x}$ equals
→Find the integral: $\int \frac{x+3}{\sqrt{5-4 x-x^{2}}} d x$
→