Question

prove that: tan^2θ−sin^2θ=tan^2θ.sin^2θ


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Answer 1

Step-by-step explanation:

this is proved that left hand side = right hand side

Answer 2

Required Answer:-

Given To Prove:

• tan²θ - sin²θ = tan²θ sin²θ

Proof:

Taking LHS,

tan²θ - sin²θ

As tan θ = sin θ/cos θ. So,

= sin²θ/cos²θ - sin²θ

= (sin²θ - sin²θ cos²θ)/(cos²θ)

Taking sin²θ as common, we get,

= sin²θ(1 - cos²θ)/(cos²θ)

= sin²θ/cos²θ × (1 - cos²θ)

= tan²θ × (1 - cos²θ) [tan θ = sin θ/cos θ]

We know that,

➡ sin²θ + cos²θ = 1

➡ sin²θ = 1 - cos²θ

So,

= tan²θ × sin²θ

= tan²θ sin²θ

= RHS (Hence Proved)

Formula Used:

• tan θ = sin θ/cos θ
• sin²θ + cos²θ = 1