Question

(sin A - cos A)(cot A + tan A) = sec A- cosec A prove that

Answer 1

(sinA - cosA)(cotA + tanA)=secA - cosecA
lhs → (sinA - cosA)[(cosA/sinA) + (sinA/cosA)]
=(sinA - cosA)(cos²A + sin²A/sinAcosA)
=(sinA - cosA)(1)/sinAcosA
=(sinA - cosA)/sinAcosA
=1/cosA - 1/sinA
=secA - cosecA
rhs → secA - cosecA
lhs=rhs
hence proved

Answer 2

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