Question

mathematics
trigonometry ​

Answer 1

Given :-

Cosec(A) - Sin(A) = x

Sec(A) - Cos(A) = y

To Prove :-

(x²y)⅔ + (xy²)⅔ = 1

Solution :-

So, Cosec(A) - Sin(A) = x

→ 1/Sin(A) - Sin(A) = x

→ (1 - Sin²A)/Sin(A) = x

→ Cos²A/Sin(A) = x

→ Cot(A).Cos(A) = x __________( i )

And, Sec(A) - Cos(A) = y

→ 1/Cos(A) - Cos(A) = y

→ (1 - Cos²A)/Cos(A) = y

→ Sin²A/Cos(A) = y

→ tan(A).Sin(A) = y ___________( i )

Now,

LHS = (x²y)⅔ + (xy²)⅔

LHS = [{Cot²A. Cos²A}.{tan(A).Sin(A)}]⅔ + [{tan²A. Sin²A}.{Cot(A).Cos(A)}]⅔

LHS = (Cos³A)⅔ + (Sin³)⅔

LHS = Sin²A + Cos²A = 1 = RHS

Hence PROVED _________"'

Hope it helps...

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