Prove that:
cos2(π4−θ)−sin2 (π4−θ)=sin 2θ
LHS=cos2(π4−θ)−sin2 (π4−θ)=cos2(π4−θ)[∵ cos 2θ=cos2 θ−sin2 θ]=cos (π2−2θ)[∵ cos (π2−θ)=sin θ]=sin 2θ = RHS
Prove that: sin(90−θ)cos(90−θ)cot(90−θ) + sin2θ = 1.
Prove the following trigonometric identities:
1+sec θsec θ=sin2 θ1−cos θ