Question

Find value of theta when cot 3 theta equals to sin 3 theta

Answer 1

Answer:

$\cot3( \alpha ) = \sin3( \alpha ) \\ \frac{ \cos(3 \alpha ) }{ \sin( 3\alpha ) } = \sin(3 \alpha ) \\ \cos( 3\alpha ) = { \sin(3 \alpha ) }^{2} \\ \cos( 3\alpha ) = 1 - { \cos( 3\alpha ) }^{2} \\ 2 { \cos( 3\alpha ) }^{2} = 1 \\ { \cos( 3\alpha ) }^{2} = \frac{1}{2} \\ \cos(3 \alpha ) = \frac{1}{ \sqrt{2} } \\ 3 \alpha = { \cos( \frac{1}{ \sqrt{2} } ) }^{ - 1} \\ \: \: \: \: \: \: \: = { \cos( \cos \frac{\pi}{4} ) }^{ - 1} \\ 3 \alpha = \frac{\pi}{4} \\ \alpha = \frac{\pi}{12}$

Answer 2

Answer:

Hey mate your answer is given below