Question

sinA-sin4A/cos4A-cosA=cot5A/2​

Answer 1

SOLUTION

TO PROVE

$\displaystyle \sf{ \frac{ \sin A - \sin 4A}{\cos 4A - \cos A} = \cot \frac{5A}{2} }$

PROOF

$\displaystyle \sf{ \frac{ \sin A - \sin 4A}{\cos 4A - \cos A} }$

$\displaystyle \sf{ = \frac{2\cos \frac{5A}{2} \: \sin \frac{3A}{2} }{2\sin \frac{5A}{2} \: \sin \frac{3A}{2} } }$

$\displaystyle \sf{ = \frac{\cos \frac{5A}{2} }{\sin \frac{5A}{2} \: } }$

$\displaystyle \sf{ = \cot \frac{5A}{2} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. if sin theta =√3/2,cos theta=-1/2 then theta lies in

https://brainly.in/question/31225531

2. value of(1+tan13)(1+tan32)+(1+tan12)(1+tan33)

https://brainly.in/question/23306292