Question

If A = 30°;
show that:
cos 2A = cos⁴ A - sin⁴ A

Answer 1

Given that A = 30°

LHS = cos 2A

= cos 2(30°)

= cos 60°

= `(1)/(2)`

RHS = `cos^4"A" – sin^4"A"`

= `cos^4 30° – sin^4 30° `

= `(sqrt3/2)^4 – (1/2)^4`

= `(9)/(16) –  (1)/(16)`

= `(1)/(2)`

LHS = RHS