Question

Hey solve this problem.
Prove this trigonometry identity :
(1+tan ^2 Q) (1+ sin Q) (1- sin Q) =1
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Answer 1

LHS =

$(1 + {tan}^{2} x) \: (1 + sinx) \: (1 - sinx) \\ \\ = ( {sec}^{2}x) \: ( {1 }^{2} - {sin}^{2} x) \\ \\ = ( {sec}^{2} x) \: ( {cos}^{2} x) \\ \\ = ( \frac{1}{ {cos}^{2}x } ) \: ( {cos}^{2} x) \\ \\ = 1$

Hope it helps.