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Question

If tan x2=mn ,then write the value of msinx+ncosx

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Solution

Given tanx2=mn

Consider,
msinx+ncosx

=m 2mn1+m2n2 + n 1m2n21+m2n2 --------------------Since, sinx=2tanx21+tan2x2 and cosx=1tan2x21+tan2x2

=2m2nm2+n2+n(n2m2)n2+m2

=n3+m2nm2+n2

=n(n2+m2)m2+n2

=n

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