Prove that the following identities :sec2θ + cosec2θ = sec2θ.cosec2θ

Taking LHS = sec2 θ + cosec2 θ [∵ cos2 θ + sin2 θ = 1]= sec2 θ × cosec2 θ =RHSHence Proved

Q16 of 268 Page 5

Prove that the following identities :
sec²θ + cosec²θ = sec²θ.cosec²θ

Taking LHS = sec² θ + cosec² θ

[∵ cos² θ + sin² θ = 1]

= sec² θ × cosec² θ

=RHS

Hence Proved

Prove the following identities :

1 – 2 cos² θ + cos⁴ θ = sin⁴θ

Prove the following identities :

1 – 2 sin² θ + sin⁴ θ = cos⁴θ

Prove that the following identities :

cotθ + tan θ = cosec θ . sec θ