Question

The general solution of sin 2x = cos 2x is ______ 

Options

• `x = npi + pi/4`

• `x = npi + pi/6`

• `x = (npi)/2 + pi/8`

• `x = npi ± pi/8`

Answer 1

The general solution of sin 2x = cos 2x is `underline(x = (npi)/2 + pi/8)`.

Explanation:

sin 2x = cos 2x

⇒ tan 2x = 1

⇒ tan 2x = tan `pi/4`

⇒ 2x = `npi + pi/4`, n ∈ Z .............[∵ tan θ = tan α ⇒ θ = nπ + α]

⇒ x =`(npi)/2 + pi/8`, n ∈ Z