NCERT Exemplar Solutions
Class 12 - Mathematics - Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS

Short Answer (S.A.)

Find the value of \( \tan^{-1}(\tan 5\pi/6) + \cos^{-1}(\cos 13\pi/6) \).

Evaluate \( \cos[\cos^{-1}(-\sqrt{3}/2) + \pi/6] \).

Prove that \( \cot(\pi/4 - 2\cot^{-1}3) = 7 \).

Find the value of \( \tan^{-1}(-1/\sqrt{3}) + \cot^{-1}(1/\sqrt{3}) + \tan^{-1}(\sin(-\pi/2)) \).

Find the value of \( \tan^{-1}(\tan 2\pi/3) \).

Show that \( 2\tan^{-1}(-3) = -\pi/2 + \tan^{-1}(-4/3) \).

Find the real solutions of the equation \( \tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^{2}+x+1} = \pi/2 \).

Find the value of the expression \( \sin(2\tan^{-1}(1/3)) + \cos(\tan^{-1}(2\sqrt{2})) \).

If \( 2\tan^{-1}(\cos \theta) = \tan^{-1}(2\csc \theta) \), then show that \( \theta = \pi/4 \).

Show that \( \cos(2\tan^{-1}(1/7)) = \sin(4\tan^{-1}(1/3)) \).

Solve the equation \( \cos(\tan^{-1} x) = \sin(\cot^{-1}(3/4)) \).