Prove the following identities :sin2θ – cos2 ϕ = sin2ϕ – cos

1.	Prove the following identities :sin2θ – cos2 ϕ = sin2ϕ – cos2θ
Answer» Taking LHS = sin² θ – cos² φ =( 1 – cos² θ) – (1 – sin² φ) [∵ cos² θ + sin² θ = 1] & [∵ cos² φ + sin² φ = 1] = 1 – cos² θ – 1 + sin² φ = sin² φ – cos² θ = RHS Hence Proved

Prove the following identities :sin2θ – cos2 ϕ = sin2ϕ – cos2θ

Answer»

Taking LHS = sin² θ – cos² φ

=( 1 – cos² θ) – (1 – sin² φ) [∵ cos² θ + sin² θ = 1] & [∵ cos² φ + sin² φ = 1]

= 1 – cos² θ – 1 + sin² φ

= sin² φ – cos² θ

= RHS

Hence Proved