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प्रश्न
Prove that (cosec A − sin A) (sec A − cos A) = `1/(tan A + cot A)`.
सिद्धांत
उत्तर
L.H.S. = (cosec A − sin A) (sec A − cos A)
= `(1/sin A − sin A/1) (1/cos A − cos A/1)`
= `((1 - sin^2A)/(sin A)) ((1 - cos^2 A)/(cos A))`
= `cos^2A/sin A xx sin^2A/cos A`
L.H.S. = cos A × Sin A
and R.H.S. = `1/(tan A+ cot A)`
= `1/(sin A/cos A + cos A/sin A)`
= `1/((sin^2 A + cos^2 A)/(sin A cos A))`
= `(sin A cos A)/1`
R.H.S. = sin A × cos A
∴ L.H.S. = R.H.S.
∴ Hence proved.
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