Question

Prove that Cos²theta(1+tan²theta)=1​

Answer 1

Answer:

Since LHS = RHS , hence Proved :)

Step-by-step explanation:

We have , LHS = cos²∅ ( 1 + tan²∅ )

= cos²∅ ( 1 + tan²∅ )

= cos²∅ .1 + tan²∅ . cos²∅

= cos ²∅ + sin²∅/cos²∅ . cos²∅

= sin²∅ + cos²∅

= 1

= RHS

Hence Proved !

Answer 2

Cos²θ(1+tan^2 θ)

(1+tan^2θ)=sec^2 θ

Hence, Cos²θ(sec^2 θ)

(sec^2 θ = 1/Cos²θ)

Hence,

Cos²θ(1/Cos²θ)=1