prove the following id

Taking out cosθ common we can write LHS,

cosθ(1/(1 - sinθ) + 1/(1 + sinθ)) =

cosθ(2/(1 - sin²θ)) =         

              ...using the identity a² - b² = (a + b)(a - b) and simplifying the fraction like 1/c + 1/d = (c + d)/cd

cosθ(2/cos²θ)) =

2/cosθ = 2 secθ = RHS.

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Team,

TopperLearning.