PrepRung
Sign inSign up free

NDA 2016 Maths · Mathematics · Inverse Trigonometric Functions · easy

The value of sin ^-13/5+sin ^-14/5 is

Single correct option

The value of sin⁡−135+sin⁡−145\sin^{-1}\dfrac35+\sin^{-1}\dfrac45 is
  1. A. π4\dfrac\pi4
  2. B. π2\dfrac\pi2
  3. C. π3\dfrac\pi3
  4. D. 3π4\dfrac{3\pi}4
Show answer and solution

Answer: (B) π2\dfrac\pi2

Because 45=1−925\dfrac45=\sqrt{1-\dfrac9{25}}, we have sin⁡−145=cos⁡−135\sin^{-1}\dfrac45=\cos^{-1}\dfrac35. So the sum is sin⁡−135+cos⁡−135=π2\sin^{-1}\dfrac35+\cos^{-1}\dfrac35=\dfrac\pi2. The two angles are about 36.9∘36.9^\circ and 53.1∘53.1^\circ, which add to 90∘90^\circ.
Report a mistake

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake