Question

If secθ= cosec30° and θ is an acute angle, find the value of 4 sin²θ - 2 cos²θ.

Answer 1

secθ= cosec30°
⇒ secθ = 2
⇒ secθ = sec60°
⇒ θ = 60°
Now,
4sin²θ - 2cos²θ
= 4sin²60° - 2cos²60°

= `4 xx (sqrt(3)/2)^2 - 2 xx (1/2)^2`

= `4 xx (3)/(4) - 2 xx (1)/(4)`

= `3 - (1)/(2)`

= `(6 - 1)/(2)`

= `(5)/(2)`.