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

Write the difference between maximum and minimum values of  sin⁻¹ x for x ∈ [− 1, 1].

If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,`  then write the value of x + y + z.

If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan⁻¹ x.

If x < 0, then write the value of cos⁻¹ `((1-x^2)/(1+x^2))` in terms of tan⁻¹ x.

Write the value of tan⁻¹x + tan⁻¹ `(1/x)`for x > 0.

Write the value of tan⁻¹ x + tan⁻¹ `(1/x)`  for x < 0.

What is the value of cos⁻¹ `(cos  (2x)/3)+sin^-1(sin  (2x)/3)?`

If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`

Write the value of sin (cot⁻¹ x).

Write the value of

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

Write the value of cos⁻¹ (cos 1540°).

Write the value of sin⁻¹

\[\left( \sin( -{600}°) \right)\].

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

Write the value of sin⁻¹ (sin 1550°).

Evaluate sin

\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]

Evaluate sin \[\left( \tan^{- 1} \frac{3}{4} \right)\]

Write the value of cos⁻¹ \[\left( \tan\frac{3\pi}{4} \right)\]

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

Write the value of cos⁻¹ (cos 350°) − sin⁻¹ (sin 350°)

Write the value of cos² \[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]