Sigma r=1 to r=7 tan square {r(pi)/16}
Equals to what?

Question

Sigma r=1 to r=7 tan square {r(pi)/16}
Equals to what?

parthkohli · Answer

Hmm, I'm getting 35...

anonymous · Answer

Yup how?

parthkohli · Answer

Have to do a lot of typing for that...

parthkohli · Answer

OK, I'll type.$$\tan^2\frac{\pi}{16} + \tan^2 \frac{2\pi}{16}  + \tan^2\frac{3\pi}{16}  + \tan^2\frac{4\pi}{16} + \cot^2 \frac{3\pi}{16} + \cot^2 \frac{2\pi}{16} + \cot^2 \frac{\pi}{16}$$

parthkohli · Answer

Now $\tan^2 4\pi/16 = 1$. We'll pair the rest like this:$$\tan^2 \pi/16 + \cot^2 \pi/16= \left(\tan \pi/16 + \cot \pi/16\right)^2 - 2$$$$= \left(\frac{1}{\sin \pi/16 \cos \pi/16}\right)^2 -2$$

parthkohli · Answer

In the end we have$$4\left(\frac{1}{\sin^2 \pi/8} + \frac{1}{\sin^2 \pi/4 } + \frac{1}{\sin
^2 3\pi/8 }\right)-5$$Now again notice $\sin^2 3\pi/8 = \cos^2 \pi/8$

parthkohli · Answer

Sorry, this website is very glitchy at the moment. Can you do the rest of the work on your own? Thanks :)

anonymous · Answer

Yaa..sure thanks a lot..got the method.

parthkohli · Answer

Great, are you in 11th?

anonymous · Answer

12th