Question

$\frac{sin \theta }{cos \theta }+\frac{sin 2 \theta }{cos^{2} \theta }+\frac{sin 3 \theta }{cos^{2} \theta }+\ldots +\frac{sin 6 \theta }{cos^{6} \theta }$ is equal to

• A. $cot\theta +\frac{cos 7 \theta }{sin\theta cos^{6} \theta }$
• B. $cot\theta -\frac{cos 7 \theta }{sin \theta cos^{6} \theta }$
• C. $\frac{cos 7 \theta }{sin \theta cos^{6} \theta }-cot\theta $
• D. $21tan\theta $

Answer 1

Answer: (B)

$cot\theta -\frac{sin \theta }{cos \theta }=\frac{cos 2 \theta }{sin \theta cos \theta }\Rightarrow \frac{cos 2 \theta }{sin \theta cos \theta }-\frac{sin 2 \theta }{cos^{2} \theta }=\frac{cos 3 \theta }{cos^{2} \theta sin \theta }$
Similarly, $\frac{cos 6 \theta }{cos^{5} \theta sin \theta }-\frac{sin 6 \theta }{cos^{6} \theta }=\frac{cos 7 \theta }{cos^{6} \theta sin \theta }$