Question

If theta=30^(@) then prove that: a.cos2 theta=cos^(2)theta-sin^(2)theta.​

Answer 1

$\huge \text{\mathbb{\underline {ANSWER \ and \ EXPLANATION}}}$

Given that,

θ = 30°

Hence,

cos2θ = cos2*30 = cos60° = 1/2

cos²θ = cos²30° = (√3/2)² = 3/4

sin²θ = sin²30° = (1/2)² = 1/4

LHS = cos2θ = cos2*30 = cos60° = 1/2

RHS = cos²θ - sin²θ = 3/4 - 1/4 = (3-1)/4 = 2/4 = 1/2

Therefore,

LHS = RHS

cos2θ = cos²θ - sin²θ

Hence, proved