Question

Please help timmed!!!!

Write the given expression as a single trigonometric function.

Tan(3pi/7)-tan2pi/5 over 1+tan3pi/7)tan(2pi/5)


A)Tan(pi/35.

B) tan 29pi/35.

C) wrong

d) tan 31pi/35

Answer 1

`\tan(\alpha - \beta) = \cfrac{\tan(\alpha)- \tan(\beta)}{1+ \tan(\alpha)\tan(\beta)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{\tan\left( (3\pi )/(7) \right)-\tan\left( (2\pi )/(5) \right)}{1+\tan\left( (3\pi )/(7) \right)\tan\left( (2\pi )/(5) \right)}\implies \tan\left( \cfrac{3\pi }{7}-\cfrac{2\pi }{5} \right) \\\\\\ \tan\left( \cfrac{(5)3\pi~~ - ~~(7)2\pi }{35} \right)\implies \tan\left( \cfrac{15\pi-14\pi }{35} \right)\implies \tan\left( \cfrac{\pi }{35} \right)`