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Question

If sin(θ+α)=cos(θ+α), then which of the following is/are correct?
where θ,α(0,π2){π4}

A
tanα=1tanθ1+tanθ
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B
tanα=1+tanθ1tanθ
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C
tanθ=1+tanα1tanα
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D
tanθ=1tanα1+tanα
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Solution

The correct option is D tanθ=1tanα1+tanα
sin(θ+α)=cos(θ+α)sinθcosα+sinαcosθ =cosθcosαsinθsinαsinθcosα+sinθsinα =cosθcosαsinαcosθ(1)sinθ(cosα+sinα)=cosθ(cosαsinα)tanθ=(cosαsinα)(cosα+sinα)tanθ=1tanα1+tanα

Now,
tanθ=1tanα1+tanαtanθ+tanαtanθ=1tanαtanα=1tanθ1+tanθ

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