Question

Q 41 step by step................

Answer 1

3).is the answer root2+root3+root4+root6

We know that, cotx = 1tanxsinx2=1−cosx2−−−−−√and cosx2=1+cosx2−−−−−√and tanx2=sinx2cosx2=2sinx2cosx22cosx2×cosx2=sinx2cos2x2=sinx1+cosxSo cot(712)=cot152=1tan152and tan152=sin152cos152=sin151+cos15[as derived above]and sin15= sin302=1−cos302−−−−−−√=1−3√22−−−−√=2−3√√2cos15= cos302=1+cos302−−−−−−√=2+3√√2So tan152=sin151+cos15=2−3√√21+2+3√√2=2−3√√2+2+3√√So cot152=2+2+3√√2−3√√×2+3√√2+3√√=(2+2+3√√)(2+3√√)4−3√=(2+2+3√−−−−−−√)(2+3√−−−−−−√)=22+3√−−−−−−√+2+3√=3√+4√+8+43√−−−−−−−√=3√+4√+2+6+212−−√−−−−−−−−−−−√=3√+4√+(2√)2+(6√)2+2×6√×2√−−−−−−−−−−−−−−−−−−−−−−−−√=3√+4√+[(2√)+(6√)]2−−−−−−−−−−−−−√=3√+4√+2√+6

I hope this can help. if not repost it with more points I will do it clearly.