Prove the following identitiestan2 φ + cot2 φ + 2 = sec2ϕ. cosec2ϕ

Taking LHS = tan2 φ + cot2 φ + 2 [∵ (a + b)2 = (a2 + b2 + 2ab)] [∵ cos2 φ + sin2 φ = 1]= sec2 φ cosec2 φ =RHSHence Proved

Q32 of 268 Page 5

Prove the following identities
tan² φ + cot² φ + 2 = sec²ϕ. cosec²ϕ

Taking LHS = tan² φ + cot² φ + 2

[∵ (a + b)² = (a² + b² + 2ab)]

[∵ cos² φ + sin² φ = 1]

= sec² φ cosec² φ

=RHS

Hence Proved

Prove the following identities

cot²θ – cos²θ = cot²θ . cos²θ

Prove the following identities

tan² φ – sin² φ – tan² φ . sin² φ = 0

Prove the following identities