\frac{\cos \\theta }{1+\sin \\theta} + {1+\sin \\theta} / {\cos \\theta}

TS ICET 23 May 2018 Shift 2 Paper

Question : 120 of 200

Marks: +1, -0

{\cos \θ }/{1+\sin \θ} + {1+\sin \θ} / {\cos \θ}

Solution:

\;{\cos θ}/{1+\sin θ}+\;{1+\sin θ}/{\cos θ}

=\;{\cos ^{2} θ+(1+\sin θ)^{2}}/{\cos θ(1+\sin θ)}

=\;{\cos ^{2} θ+1+\sin ^{2} θ+2 \sin θ}/{\cos θ(1+\sin θ)}

=\;{2(1+\sin θ)}/{\cos θ(1+\sin θ)}=2 \sec θ

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