Question

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

Answer 1

L.H.S=(cosec A-sin A)(sec A-cos A)

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

=[(1-sin²A)/sin A][(1-cos² A)/cos A]

=cos²A/sin A.sin²A/cos A

=sin A. cos A

R.H.S=1/(tan A+cot A)

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

            =1/(sin²A+cos²A)/cos A. sin A

            =cos A.sin A

hence, L.H.S.=R.H.S.

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