Question

prove that , 1+cos A - sin A /1- cosA-sinA=1- sin A /cos A

Answer 1

sinA/1-cosA =1 +cosA/sinA

L.H.S= sinA/1-cosA

=sinA(1+cosA)/(1-cosA)(1+cosA)

=sinA(1+cosA)/1-cos^2(A)

=sinA(1+cosA)/sin^2(A)

=1 +cosA/sinA

=R.H.S



We have to prove:

sinA/(1 - cosA) = (1 + cosA)/sinA

To do this we multiply both sides of equation by (1 - cosA)*sinA, giving

[sinA/(1 - cosA)]*[(1 - cosA)*sinA] = [(1 + cosA)/sinA]*[(1 - cosA)*sinA]

Therefor:

sinA^2* = (1 + cosA)*(1 - cosA)

Therefore:

sinA^2* = 1 - cosA^2

Shifting the term cosA^2 from right hand side to left hand side in the above equation we get:

sinA^2* + cosA^2 = 1

We know above relationship to be true. Therefor the given equation is true.

Answer 2

Step-by-step explanation:

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