Question

prove that (cosec ∅ - sin∅) ( sec∅ - cos ∅)= 1/tan ∅+ cot∅

Answer 1

Hola there,

Let ∅ be 'A'

Given => (cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)

LHS

=> (cosecA - sinA)(secA - cosA)

=> (1/sinA - sinA)(1/cosA - cosA)

=> [(1 - sin²A)/sinA][(1 - cos²A)/cosA]

=> (cos²A/sinA)(sin²A/cosA)

=> sinAcosA/1

=>(sinAcosA)/(sin²A + cos²A)

=> 1/[(sin²A/sinAcosA) + (cos²A/sinAcosA)]

=> 1/(tanA + cotA)

=> RHS

LHS = RHS

Hence Proved

Hope this helps....:)

Answer 2

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