Question

If sec 0 - tan = 5 and
coseco – cot 0 = 3 then
(sec 0+tan 8) (cosec 0 + cot e​

Answer 1

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ANSWER

Given x=secθ−tanθ=

cosθ

1−sinθ

y=cosec θ+cotθ=

sinθ

1+cosθ

xy+1=(

cosθ

1−sinθ

)(

sinθ

1+cosθ

)+1=

sinθcosθ

1−sinθ+cosθ

=

sinθcosθ

(sin

2

θ+cos

2

θ)

−

sinθcosθ

(sinθ−cosθ)

=(tanθ+cotθ)−(secθ−cosec θ)

=(cosec θ+cotθ)−(secθ−tanθ)=y−x

∴ xy+1=y−x.

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