Question

given cot theta equal to 7 by 8 then evaluate 1 + sin theta into 1 minus sin theta by 1 + cos theta into 1 minus cos theta

Answer 1

Given that : Cotθ = 7/8 = b/p

now we have to evaluate: (1+sinθ) (1-sinθ )/ (1+cosθ) (1-cosθ)

by using the Pythagoras theorem

h = √p²+b²

therefore h  = √49+64 = √113

∴ sinθ p/h = 8/√113 and Cosθ = b/h = 7/√113

now (1+sinθ) (1-sinθ) / ( 1+cosθ) (1-cosθ) = (1-sin²θ)/ (1-cos²θ)

= (1-(8/√113)²) / (1-(7/√113)²) = 1-64/113 / 1-49-113

= 49/64

Hence  (1+sinθ) (1-sinθ) / (1+cosθ) (1-cosθ)  = 49/64

Answer 2

Answer:

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