सिद्ध कीजिए कि `(cosec A - sin A ) ( sec A - cos A) = 1/(tan A + cot A)`

Explanation

L.H.S. ` = ( cosec A - sin A ) (sec A - cos A ) `
` = (1/(sin A )- sin A )(1/(cos A) - cos A) = ((1-sin^(2)A)/(sin A)) ((1-cos^(2)A)/(cos A))`
` = (cos^(2) A)/(sin A) * ( sin ^(2) A)/(cos A) = sin A cos A ` ....(i)
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 " "[:' sin ^(2) A+ cos^(2) A = 1]`
` = sin A cos A ` ...(ii)
`:. `(i)और (ii) ,से L.H.S = R.H.S
अतः ` (cosec A - sin A)(sec A - cos A) = 1/(tan A = cot A)`