Question

Prove that cosA+sinA/cosA-sinA -cosA-sinA/cosA+sinA=2tanA

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{cos(A)+sin(A)}{cos(A)-sin(A)}-\dfrac{cos(A)-sin(A)}{cos(A)+sin(A)}}$

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

$\sf{=\dfrac{4\,cos(A)\,sin(A)}{cos^2(A)-sin^2(A)}}$

$\sf{=\dfrac{2\cdot2\,sin(A)\,cos(A)}{cos^2(A)-sin^2(A)}}$

$\sf{=\dfrac{2\,sin(2A)}{cos(2A)}}$

$\sf{=2\,tan(2A)}}$

Answer 2

Answer:

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