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(sinA-cosA+1)/(sinA+cosA-1)=2(1+cosecA)​

User Printemp
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Answer:

The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0

Explanation:

Given Trigonometrical function as :


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

Or,
(sin A + ( 1 - cos A))/(sin A - (1 - cos A)) = 2 (1 + cosec A)

, Now, rationalizing


((sin A + ( 1 - cos A)) * (sin A + (1 - cosA)))/((sin A - (1 - cos A))* (sin A + (1 - cos A))) = 2 (1 + cosec A)

Or,
((sin A + (1 - cos A))^(2))/(sin^(2) - (1-cos A)^(2)) = 2 ( 1 +
(1)/(\textrm sinA)

Or,
(sin^(2)A + (1 - cosA)^(2) + 2 * sin A * (1 - cos A))/(sin^(2)A - (1 + cos^(2)A - 2 cos A)) = 2 (
(1 + sin A)/(sin A)

Or,
(sin^(2)A + 1 + cos^(2)A - 2 cos A + 2 sin A - 2 sin A cos A)/(sin^(2)A - 1 - cos^(2)A +2 cos A) = 2 (
(1 + sin A)/(sin A)

Or,
(sin^(2)A + 1 + cos^(2)A - 2 cos A + 2 sin A - 2 sin A cos A)/(sin^(2)A - (sin^(2)A + cos^(2)A) - cos^(2)A +2 cos A) = 2 (
(1 + sin A)/(sin A)

Or,
(2- 2 cos A + 2 sin A - 2 sin A cos A)/(- 2cos^(2)A +2 cos A) = 2 (
(1 + sin A)/(sin A)

Or,
(1-  cos A +  sin A -  sin A cos A)/(- cos^(2)A + cos A) = 2 (
(1 + sin A)/(sin A)

Or,
((1-  cos A) +  sin A (1-cos A))/(cos A(1 - cos A)) = 2 (
(1 + sin A)/(sin A)

Or,
((1-  cos A) (1 + sinA))/(cos A(1 - cos A)) = 2 (
(1 + sin A)/(sin A)

Or,
((1 + sinA))/((cos A)) = 2 (
(1 + sin A)/(sin A)

Or, sin A + sin² A = 2 cos A (1 + sin A)

Or, sin A + sin² A = 2 cos A + 2 cos A × sin A

Or, sin² A + sin A - 2 cos A - 2 cos A × sin A = 0

So,The trigonometrical expression is sin² A + sin A - 2 cos A - 2 cos A × sin A = 0 Answer

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