Simplify cos²θ(1 + tan²θ).

Solution:

It is given that

cos²θ(1 + tan²θ)

We know that tan θ = sin θ/ cos θ

= cos²θ (1 + sin²θ/ cos²θ)

Taking LCM

= cos²θ [(cos²θ + sin²θ)/ cos²θ]

We know that cos²θ + sin²θ = 1

Substituting it we get

= cos²θ (1/cos²θ)

So we get

= 1

Therefore, by simplification we get 1.

Simplify cos²θ(1 + tan²θ).

Summary:

Simplifying cos²θ(1 + tan²θ) we get 1.