Question

show that 1-tan^2theta /cot^2theta -1 =tan^2theta​

Answer 1

To Prove :-

• ( 1 - tan²θ) / (cot²θ - 1) = tan²θ

Formula used :-

• tan²θ = (sin²θ)/(cos²θ)
• cot²θ = (cos²θ)/(sin²θ)

Solution :-

Solving LHS :-

→ ( 1 - tan²θ) / (cot²θ - 1)

Putting value of tan²θ & cot²θ we get ,

→ [ 1 - (sin²θ)/(cos²θ) ] / [ (cos²θ)/(sin²θ) - 1 ]

Taking LCM ,

→ [ ( cos²θ - sin²θ) / cos²θ ] / [ ( cos²θ - sin²θ) / sin²θ ]

→ [ ( cos²θ - sin²θ) / cos²θ ] * [ sin²θ / ( cos²θ - sin²θ) ]

→ ( sin²θ / cos²θ )

→ tan²θ = RHS (Hence, Proved).

Answer 2

The solution is in the attachment.....