Question

Find the value of sin3θ/(1+2cos2θ)

cos

cos

sin

cos

• A. cos
• B. cos
• C. sin
• D. cos

Answer 1

Answer: (B), (C)

The correct options are
B

cos

C

sin

sin3θ/(1+2cos2θ)

Substituting the value of sin3θ & cos2θ

= (3sinθ−4sin³θ)/(1+2[2cos²θ−1])

= (3sinθ−4sin³θ)/(1+4cos²θ−2)

= (3sinθ−4sin³θ)/(4cos²θ−1)

How to simplify it further?

We know, sin²θ+cos²θ=1.We will replace 1 with sin²θ+cos²θ

So,

Expression = (3sinθ−4sin³θ)/(4cos²θ−sin²θ−cos²θ)

= (3sinθ−4sin³θ)/(3cos²θ−sin²θ)

= (3sinθ−4sin³θ)/(3(1−sin²θ)−sin²θ)

= sinθ(3−4sin²θ)/(3−3sin²θ−sin²θ) = sinθ(3−4sin²θ)/(3−4sin²θ) = sinθ

Note : Using the formula cos2θ = 1 - 2sin²θ will help in reducing the number of steps.