SarkariPYQ

SSC CHSL 2021 PYQ — Question 55

SSC CHSL - 4 Aug 2021 - Shift 3 • Quantitative Aptitude • Q55

Back to paper

If 2cos2θ = 3(1- sinθ), 0° < θ < 90°, then what is the value of (tan2θ + cosec3θ - sec2θ)?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e.  3\sqrt{3} - 1.

2cos2θ = 3(1- sinθ)

2(1 + sinθ)(1- sinθ) = 3(1- sinθ)

sinθ = 1/2 = 30°

(tan2θ + cosec3θ - sec2θ) = (tan2 × 30° + cosec3 × 30° - sec2 × 30°)

= 3\sqrt{3} + 1 - 2

=    3\sqrt{3} - 1