Question

(sina+sin2a)÷cosa-cos2a=cot a/2​

Answer 1

Step-by-step explanation:

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(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)

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Answer 2

Answer:

Step-by-step explanation:

(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).