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prove that:
sinA + sin^2A / cosA - cos2A=cotA/2
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Answered by
4
Answer:
sin A + sin 2A) / (cos A - cos 2A)
= (sin A + 2 sin A cos A) / (cos A - 2 cos² A + 1)
= sin A (1 + 2 cos A) / [(2 cos A + 1) (-cos A + 1)]
= sin A / (1 - cos A)
= 2 sin (A/2) cos (A/2) / (1 - 1 + 2 sin² (A/2))
= 2 sin (A/2) cos (A/2) / (2 sin² (A/2))
= cos (A/2) / sin (A/2)
= cot (A/2).
Answered by
0
Answer:
Step-by-step explanation:
(sin A + 2 sin A cos A) / (cos A - 2 cos² A + 1)
sin A (1 + 2 cos A) / [(2 cos A + 1) (-cos A + 1)]
sin A / (1 - cos A)
2 sin (A/2) cos (A/2) / (1 - 1 + 2 sin² (A/2))
2 sin (A/2) cos (A/2) / (2 sin² (A/2))
cos (A/2) / sin (A/2)
cot (A/2).
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