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Question

Prove: 2sin135=tan1247

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Solution

Let sin135=xsinx=35.

cosx=1(35)2=45

tanx=34

x=tan134sin135=tan134

Now, we have:
L.H.S.=2sin135=2tan134
=tan1⎜ ⎜ ⎜ ⎜ ⎜2×341(34)2⎟ ⎟ ⎟ ⎟ ⎟,[2tan1x=tan12x1x2]

=tan1⎜ ⎜3216916⎟ ⎟=tan1(32×167)

=tan1247

=R.H.S.

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