Question

Prove that
sec theta - 1 / tan theta = tan theta/2

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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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$\large\bold\red{To \: prove :- }$

$\large\bold\red{ \frac{secθ \: - 1}{tanθ} = tan \frac{θ}{2} }$

Identity used :-

$1. \: sinθ = 2sin \frac{θ}{2} cos \frac{θ}{2} \\ 2. \: 1 - cosθ = 2 {sin}^{2} \frac{θ}{2}$

$\large\bold\red{Solution}$

Consider LHS :-

$\frac{secθ \: - 1}{tanθ} \\ = \frac{ \frac{1}{cosθ} - 1}{ \frac{sinθ}{cosθ} } \\ = \frac{1 - cosθ}{sinθ} \\ = \frac{2 {sin}^{2} \frac{θ}{2} }{2sin \frac{θ}{2} cos \frac{θ}{2}} \\ = tan \frac{θ}{2}$

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