Question

$\frac{sin\theta }{cos\theta }+\frac{sin2\theta }{co{s}^2\theta }+\frac{sin3\theta }{co{s}^2\theta }+\dots +\frac{sin6\theta }{co{s}^6\theta }$ is equal to

• A. $cot\theta +\frac{cos7\theta }{sin\theta co{s}^6\theta }$
• B. $cot\theta -\frac{cos7\theta }{sin\theta co{s}^6\theta }$
• C. $\frac{cos7\theta }{sin\theta co{s}^6\theta }-cot\theta$
• D. $21tan\theta$

Answer 1

Answer: (B)

$cot\theta -\frac{sin\theta }{cos\theta }=\frac{cos2\theta }{sin\theta cos\theta }\Rightarrow \frac{cos2\theta }{sin\theta cos\theta }-\frac{sin2\theta }{co{s}^2\theta }=\frac{cos3\theta }{co{s}^2\theta sin\theta }$
Similarly, $\frac{cos6\theta }{co{s}^5\theta sin\theta }-\frac{sin6\theta }{co{s}^6\theta }=\frac{cos7\theta }{co{s}^6\theta sin\theta }$