Question

(sinA/1-cosA)-(sinA/1+cosA)=2cotA

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

(sin A/1-cos A)-(sin A/1+cos A) =

first we take sin A /1-cos A

multiply numerator and denominator by 1+cos A

sin A(1+cos A) sin A (1+cos A) sinA(1+cosA)

_____________ = ____________ = _________

(1-cos A)(1+cos A) (1-cos ^2 A) sin^2 A

= (1+cos A)/sin A

= 1/sin A + cos A/sin A

= cosec A + cot A ==== > (1)

similarly sin A/1+cos A

multiply numerator and denominator by 1-cos A

sin A(1-cos A) sin A(1-cos A) sin A(1-cos A)

______________ = ____________ = ___________

(1-cos A)(1+cos A) (1- cos ^ 2 A) sin ^2 A

= (1-cos A)/sin A

= 1/sin A - cos A/sin A

= cosec A - cot A ======> (2)

subtract (1) from (2),we get

(sin A/1-cos A) - (sin A/1+cos A) = 2 cot A

hence proved.

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