Question

Prove that :- {(1+sinA-cos A) / (1+sinA+cos A)}^2=(1-cosA) / (1+cos A)

Answer 1

Answer:

On the left side of the equation

Write CosA ( numerator) as 1–(2 sin^2 {A/2})

Write Cos A (denominator) as (2 cos^2{A/2})-1

Write Sin A as {2 Sin(A/2) Cos (A/2)}

We get

1 - [1–(2 sin^2 {A/2})] + 2 Sin(A/2) Cos(A/2) whole squared in the numerator

And

1 + [(2 cos^2{A/2})-1]+ 2 Sin(A/2) Cos(A/2) whole squared in the denominator

[2 Sin (A/2) {Sin(A/2)+ Cos(A/2)}/ 2 Cos (A/2){Sin(A/2)+ Cos(A/2)}]^2

Cancelling out the common parts - [2{Sin(A/2)+ Cos(A/2)}]^2

We get tan^2 (A/2)

Write it as Sin^2(A/2)/Cos^2(A/2)

Multiply by 2 on the numerator and denominator

Add and subtract 1, on the numerator and denominator

1–1+2 Sin^2(A/2)/1+ 2Cos^2(A/2)-1

1-{1- 2Sin^2(A/2)}/ 1+ {2Cos^2(A/2)-1}

We know that 1- 2Sin^2(A/2) can be written as Cos A

And 2Cos^2(A/2)-1 can also be written as Cos A

So, we get 1- CosA/1+ SinA, which is the required result.

Answer 2

Answer:

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