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Question

If tan x2=mn, then write the value of m sin x + n cos x.

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Solution

We have,

tanx2=mn sin x2cos x2=mn sinx2=mk, and cos x2=nk (say)

Now,

m sin x + n cos x

=m.2 sin x2. cos x2+n (cos2 x2sin2 x2)=2m. mk. nk+n (n2k2m2k2)=2m2 k2 n+nk2(n2m2)=nk2 (2m2+n2m2)=nk2 (m2+n2)=n (m2k2+n2k2)=n(sin2x2+cos2x2)
=n


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