Question

cos²θ(1 + tan²θ) = 1, Prove it

Answer 1

According to identity 1+tan^2theta=sec^2theta
So now we have cos^2theta×sec^2theta
We know we can write cos^2theta to 1/sec^2 theta
So it will be cancelled and answer will be 1

Answer 2

Step-by-step explanation:

As per the question,

We have been prove that cos²θ(1 + tan²θ) = 1

Consider LHS, we have

cos²θ(1 + tan²θ)

Now,

By using the trigonometric identity

sin²θ + cos²θ = 1

tanθ = sinθ/cosθ

We can write by putting the value of tanθ.

∴ cos²θ(1 + tan²θ)

cos²θ(1 + (sinθ/cosθ)²)

= sin²θ + cos²θ

= 1

= RHS

Therefore,

LHS = RHS

Hence, proved.