Question

Qno.96
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Answer 1

given, cosec x - sin x = l ---( 1 )and sec x - cos x =m----(2)

now, 1 -->  1-sin^2x / sin x = cos^2 x / sin x = l

similarly, (2) implies, sin^2 x / cos x = m

substituting these forms in the given condition,

we get, (cos^2 x / sin x )^2 .(sin^2 x / cos x)^2 . [ (cos^2 x / sin x )^2 + (sin^2 x / cos x)^2 + 3 ]

=> cos^2 x . sin ^2 x. [ (cos ^4 x / sin^2 x ) + ( sin^4 x / cos^2 x ) + 3]

=> cos^6x + sin^6x + 3 .cos^2 x . sin ^2 x.

=>  1 - 3.cos^2 x . sin ^2 x + 3.cos^2 x . sin ^2 x = 1.

hence proved.