SarkariPYQ

SSC CHSL 2019 PYQ — Question 62

SSC CHSL - 2nd July 2019 - Shift 2 • Quantitative Aptitude • Q62

Back to paper

If 3sinθ = 2cos2θ, 0° < θ < 90°, then the value of (tan θ + cos θ + sin θ) is:

Show answer & explanation

Correct answer: D

Explanation

Correct Answer is option 4 i.e. (5 + √3)/2√3

Understanding

Application

Given:

3sinθ = 2cos2θ, 0° < θ < 90°

3sinθ = 2cos2θ

3sinθ = 2(1 – Sin2θ)

2Sin2θ + 3sinθ – 2 = 0

(2sinθ – 1) (Sinθ + 2) = 0

Sinθ = ½

Then, θ = 30

Now,

(tan θ + cos θ + sin θ)

Putting θ = 30:

tan 30 + cos 30 + sin 30

= (1/√3) + (√3/2) + (1/2) = (5 + √3)/2√3