Question

Prove that 1-cosA/sinA=tan(A/2)

Answer 1

Step-by-step explanation:

using identity...it's simple...

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Answer 2

step by step: L.H.S=1‐cosA/sinA

=[CosA÷(1-sinA)]÷[(1+sinA)÷(1+sinA)]

=cosA(1+sinA)÷(1-sinA)²

=cosA(1+sinA)÷cos²A

=(1+sinA)÷cosA

=[Cos²(A/2)+Sin²(A/2)+2sin(A/2)cos(A/2)]÷[cos²(A/2)-sin²(A/2)]

=[cos(A/2)+sin(A/2)]÷[cos(A/2)-sin(A/2)]

=[1+tan(A/2)]÷[1+tan(A/2)]

=[tan45⁰+tan(A/2)]÷[1-tan45⁰tan(A/2)]

=tan(45⁰+A/2)=R.H.S(proved)