Question

(cosec A - sin A) (sec A - cos A) =
tan A + cot A​

Answer 1

LHS = (cosec A - sinA) (Sec A - cos A)

LHS = (1/sinA - sinA) (1/cosA - cosA)

LHS = (1-sin²A/sinA) (1-cos²A/cosA)

LHS = (cos²A/sinA)(sin²A/cosA

LHS = cosA × cosA__________(1)

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RHS = 1/tanA+cotA

RHS = 1/(sinA/cosA + cosA/sinA

RHS = 1/(sin²A+cos²A/cosA×sinA)

RHS = 1/(1/cosA×sinA)

RHS = 1×(cosA×sinA)

RHS = cosA×sinA ________(2)

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by comparing equation (1) and (2) we can said that ,

LHS = RHS

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Answer 2

(cosec a -sina)(seca-cosa)

(1/sina-sins)(1/cosa-cosa)

1-sin2a(1-cos2a)

then 1/sin2a is tana

1/cos2a is cot a