Question

$Generalsolutionoftan5\theta =cot2\theta is$

• A. $\frac{n\pi }{7}+\frac{\pi }{2},n\in Z$
• B. $\theta =\frac{n\pi }{7}+\frac{\pi }{3},n\in Z$
• C. $\theta =\frac{n\pi }{7}+\frac{\pi }{14},n\in Z$
• D. $\theta =\frac{n\pi }{7}-\frac{\pi }{14},n\in Z$

Answer 1

The correct option is C

$\theta =\frac{n\pi }{7}+\frac{\pi }{14},n\in Z$

$Given:tan5\theta =cot2\theta \Rightarrow tan5\theta =tan(\frac{\pi }{2}-2\theta )\Rightarrow 5\theta =n\pi +\frac{\pi }{2}-2\theta \Rightarrow 7\theta =n\pi +\frac{\pi }{2}\Rightarrow \theta =\frac{n\pi }{7}+\frac{\pi }{14},n\in Z$