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Question

If tanθ=45, find the value of cosθsinθcosθ+sinθ.

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Solution

given tan(θ)=4/5
cosθsinθcosθ+sinθ=1sinθcosθ1+sinθcosθ=1tanθ1+tanθ
[dividing with cos(θ) in numerator and denominator]

therefore now substituting the value we get
14/51+4/5=1/59/5=19

therefore the required value is 19

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