Question

If sin 4A – cos 2A = cos 4A – sin 2A `("where", 0 < A < π/4)`, then the value of tan 4A is ______.

विकल्प

• 1

• `1/sqrt(3)`

• `sqrt(3)`

• `(sqrt(3) - 1)/(sqrt(3) + 1)`

Answer 1

If sin 4A – cos 2A = cos 4A – sin 2A `("where", 0 < A < π/4)`, then the value of tan 4A is `underlinebb(sqrt(3))`.

Explanation:

sin 4 A – cos 4 A = cos 2 A – sin 2 A

On squaring both sides, we.get

1 – 2 sin 4 A cos 4 A = 1 – 2 sin 2 A cos 2 A

`\implies` cos 4 A = `1/2`

`\implies` tan 4 A = `sqrt(3)`