The minimum values of 1 − 4 sin x cos x is

Question

Question

Answer 1

Concept:

-1 ≤ sin θ ≤ 1

sin 2 θ = 2 sin θ cos θ

Calculation

We have to find the minimum value of 1 − 4 sin x cos x

Let f(x) = 1 − 4 sin x cos x

= 1 – 2 × (2 sin x cos x)

= 1 – 2 sin 2x (∵sin 2θ = 2 sin θ cos θ)

For minimum value of f(x), sin 2x should be maximum

As we know that,

Maximum value of sin θ is 1, so maximum value of sin 2x is 1

Therefore, Minimum value of f(x) = 1 – 2 × 1 = -1