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 prove that i)cos?cosec?sin?sec?/co...
 Entrance Exam
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prove that i)cos?cosec?sin?sec?/cos?+sin?=cosec?sec? ii)cot^2?(sec?1)/(1+sin?)=sec^2?(1sin?)/(1+sec?) iii)(1cos?)^1/2/(1+cos?)^1/2=sin?/1+cos? iv)(1+sin?)^1/2/(1sin?)^1/2=cos?/1sin?
L.H.S.
= cos A . cosec A  sin A . sec A / cos A + sin A
= [(1 / sec A) . cosec A  (1 / cosec A) . sec A ] / [(1 / sec A) + (1 / cosec A) ]
= [cosec A / sec A  sec A / cosec A ] / [ cosec A + sec A / sec A . cosec A ]
= [cosec^{2} A  sec^{2} A / sec A . cosec A ] / [ cosec A + sec A / sec A . cosec A ]
= (cosec^{2} A  sec^{2} A) (sec A . cosec A) / sec A . cosec A (sec A + cosec A)
= (cosec A  sec A) (cosec A + sec A) / (sec A + cosec A)
= cosec A  sec A
= R.H.S.