Question

prove that cos²θ+tan²θ=1

Answer 1

Answer:

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.

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