Math, asked by dudleyandrew003, 1 year ago

prove that sinA/1+cosA+sinA/1-cosA=2secA

Answers

Answered by wwwHarshSable
2

Answer:

Step-by-step explanation:

Pl mark it the brainliest answer if it helps you to get satisfaction.

Dear Pl check out if ur question is right??

Coz RHS comes out to be 2cosecA

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Answered by virtuematane
2

Answer:

on solving the left hand side of the expression:

\dfrac{\sin A}{1+\cos A}+\dfrac{\sin A}{1-\cos A}

on taking the l.c.m of the above expression we get:

\dfrac{\sin A(1-\cos A)+\sin A(1+\cos A)}{(1-\cos A)(1+\cos A)}\\\\=\dfrac{\sin A-\sin A \cos A+\sin A+\sin A\cos A}{1-\cos^2A}\\\\=\dfrac{\sin A+\sin A}{\sin^2 A}

since on cancelling the same term with opposite signs in the numerator.

=\dfrac{2\sin A}{\sin^2 A}\\\\=\dfrac{2}{\sin A}\\\\=2 cosec A

Hence, the equality is written as:

\dfrac{\sin A}{1+\cos A}+\dfrac{\sin A}{1-\cos A}=2 cosec A

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