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

If tan⁻¹ x + tan⁻¹ y = `pi/4`,  then write the value of x + y + xy.

Write the value of cos⁻¹ (cos 6).

Write the value of sin⁻¹ \[\left( \cos\frac{\pi}{9} \right)\]

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

Write the value of tan⁻¹\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]

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

Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]

Write the value of cos⁻¹ \[\left( \cos\frac{5\pi}{4} \right)\]

Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]

Evaluate: \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]

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 \[\tan^{- 1} 1 + \cos^{- 1} \left( - \frac{1}{2} \right)\]