Prove the following identities :sin2 θ(1+ cot2 θ) = 1

Taking LHS = sin2 θ(1+ cot2 θ)= sin2 θ (cosec2 θ) [∵ cot2 θ +1= cosec2 θ ]= 1=RHSHence Proved

Q14 of 268 Page 5

Prove the following identities :
sin² θ(1+ cot² θ) = 1

Taking LHS = sin² θ(1+ cot² θ)

= sin² θ (cosec² θ) [∵ cot² θ +1= cosec² θ ]

= 1

=RHS

Hence Proved

Prove the followings identities:

Prove the following identities :

sinθ. cotθ = cos θ

Prove the following identities :

cos² A (tan² A+1) = 1

Prove the following identities :

tan⁴θ + tan²θ = sec⁴θ – sec²θ