Question

prove that: tan A +1/tanA = secA. cosecA

Answer 1

you can see your answer

Answer 2

$LHS = tan A + \frac{1}{tan A } \\= \frac{tan^{2} A + 1}{tanA } \\= \frac{ sec^{2} A }{tanA }$

$\boxed {\pink { Since, 1+ tan^{2} A = sec^{2} A }}$

$= \frac{ \frac{1}{cos^{2} A }}{\frac{sinA}{cos A}} \\= \frac{1}{cos^{2} A} \times \frac{ cos A}{sinA } \\= \frac{1}{cos A } \times \frac{1}{sinA} \\= sec A Cosec A \\= RHS$

$LHS = RHS$

$Hence \:proved$

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