Question

Prove that : tan theta + sec theta = 1/sec theta - tan theta
First understanding answer will be marked as the branlilast

Answer 1

Step-by-step explanation:

To prove tanθ+secθ = 1 / (secθ-tanθ)

take LHS = tanθ + secθ

= (tanθ + secθ) [ (secθ-tanθ)/(secθ-tanθ)]

= [  (secθ+tanθ) (secθ-tanθ)]  / (secθ-tanθ)

= (sec²θ-tan²θ) / (secθ-tanθ)

= 1/(secθ-tanθ)            [ ∵ sec²θ-tan²θ = 1 ]

= RHS

LHS = RHS

hence proved

Answer 2

Answer:

LHS = tanθ + secθ

= (tanθ + secθ) [ (secθ-tanθ)/(secθ-tanθ)]

= [(secθ+tanθ) (secθ-tanθ)]  / (secθ-tanθ)

= (sec²θ-tan²θ) / (secθ-tanθ)

= 1/(secθ-tanθ)            [ ∵ sec²θ-tan²θ = 1 ]

= RHS

LHS = RHS

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