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Question

The value of tan(π4+θ)×tan(3π4+θ) is:

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Solution

tan(π4+θ)×tan(3π4+θ)
tan(x)=cot(π2x)
tan(π4+θ)tan(3π4+θ)
=tan(π4+θ)cot(π2(π4+θ))
=tan(π4+θ)cot(π4θ)
=tan(π4+θ)(cot(π4+θ))
=1

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