38. (1 + cot A-cosec A) (1 + tan A + sec A) = 2
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Step-by-step explanation:
LHS
(1 + cot A - cosec A ) ( 1 + tan A + sec A )
= (1 + cos A / sin A - 1 / sin A ) ( 1 + sin A / cos A + 1 / cosA )
= 1 + cos A - 1 / sin A × 1 + sinA + 1 / cosA
= (SinA + cosA - 1 / sinA ) ( cos A + sinA + 1 / cosA )
= (SinA + cosA )^2 - 1 / sinA × cosA
= sin^2 A + cos^2 A + 2sinA × cosA -1 / sinA × cosA
= 1 + 2 - 1
= 2
RHS
2
LHS = RHS ( hence proved )
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