Question

(cosec A - sin A) (sec A-cos A) = 1÷ tan A + cot A​

Answer 1

Lhs =(coseca-sina)(seca-cosa)

1/sina-sina. 1/cosa-cosa

1/sina

(1-sin2a)/sina. (1-cos2a)/cosa

cos2a/sina. sin2a/cosa

sina cosa

Rhs =1/tana+cot a

1/sina/cosa+cosa/sina

1/sin2a+ cos2a/sinacosa

1/1/sina cosa

sina cosa

hence we proved

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Answer 2

Let us solve the problem,

(Cosec A - sinA)( Sec A - Cos A)

= 1÷ Tan A+ cot A

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

=(1- sin²A/sin A )(1- cos²A/Cos A)

=Cos²A/sin A* sin²A/cosA

{ 1- sin²A = cos²A and vice versa}

=CosAsinA

RHS= { given in the picture attached with it}