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Question

Prove that tan(3π4+θ)tan(π4+θ)=1

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Solution

Consider the L.H.S.

=tan(3π4+θ)tan(π4+θ)

We know that,

tan(A+B)=tanA+tanB1tanAtanB

Therefore,

=⎜ ⎜ ⎜tan3π4+tanθ1tan3π4×tanθ⎟ ⎟ ⎟⎜ ⎜tanπ4+tanθ1tanπ4×tanθ⎟ ⎟

Since,

tan3π4=1

tanπ4=1

Therefore,

=(1+tanθ1+tanθ)(1+tanθ1tanθ)

=(1+tanθ1tanθ)

=(1tanθ1tanθ)

=1

R.H.S

Hence, proved.


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