Question

Question 24 Prove that cos 4x = 1 – 8sin2 x cos2 x

Class X1 - Maths -Trigonometric Functions Page 74

Answer 1

LHS = cos4x
= cos2(2x)
use the formula,
cos2∅ = 1 - 2sin²∅

= 1 - 2sin²2x
Now, use the formula,
sin2∅ = 2sin∅.cos∅

= 1 - 2(2sinx.cosx)²
= 1 - 2×4sin²x.cos²x
= 1 - 8sin²x.cos²x = RHS