PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.

If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.

Write the value of \[\sin^{- 1} \left( \frac{1}{3} \right) - \cos^{- 1} \left( - \frac{1}{3} \right)\]

If 4 sin⁻¹ x + cos⁻¹ x = π, then what is the value of x?

If x < 0, y < 0 such that xy = 1, then write the value of tan⁻¹ x + tan⁻¹ y.

What is the principal value of `sin^-1(-sqrt3/2)?`

Write the principal value of `sin^-1(-1/2)`

Write the principal value of \[\cos^{- 1} \left( \cos\frac{2\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{2\pi}{3} \right)\]

Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]

Write the principal value of \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]

Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]

Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`

Write the principal value of \[\cos^{- 1} \left( \cos680^\circ  \right)\]

Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]

Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]

Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]

Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]

Wnte the value of the expression \[\tan\left( \frac{\sin^{- 1} x + \cos^{- 1} x}{2} \right), \text { when } x = \frac{\sqrt{3}}{2}\]

Write the principal value of \[\sin^{- 1} \left\{ \cos\left( \sin^{- 1} \frac{1}{2} \right) \right\}\]

The set of values of `\text(cosec)^-1(sqrt3/2)`