prove that 1+sinA-cosA/1+sinA+cosA=tan(A/2
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Answer:
Step-by-step explanation:
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14
Answer:
1+sinA-cosA/1+sinA+cosA=tanA/2
Step-by-step explanation:
L.H.S
1+sinA-cosA/1+sinA+cosA×1+sinA-cosA/1+sinA-cosA
=((1+sinA)-cosA)²/(1+sinA)²-(cosA)1
=(1+sinA)1+cos²A-2(1-sinA)cosA/1+sin²A-2sinA-(1-sin²A)
=2+2sinA-2cosA-(1-sin²A)-2cosA-2sinAcosA/1+sin²A+2sinA
=2(1-cosA)(1+sinA)/2sinA(1+sinA)
2(1-cosA)(1+sinA)/2sinA(1+sinA)
=1-cosA/sinA
2sin²/2×A/2sinA/×cosA/2
since cos2x=1-2sin²x and sin 2x=2sinx cosx)
therefore tanA/2
R.H.S.
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