What is the exact value of cos 5° + cos 77° + cos 149° + cos 221° + cos 293°?
1Adding cos 5 and cos 293 together; and adding cos 77 and cos 221 together .....
2 cos(149)cos(144) + 2 cos(149)cos(72) + cos(149)
cos(149) [ 2 cos(144) + 2 cos(72) + 1 ]
cos(149) [ 2{ 2 cos272 -1 } + 2 cos(72) + 1 ]
cos(149) [ 4 cos2(72) + 2 cos(72) - 1 ]
However I'm not very sure of my logic .... so I would advise u to get it checked by NISHANT SIR .....
1cos5 + cos77 + cos149 + cos221 + cos293
= cos5 + cos77 + cos(90+59) + cos(180+41) + cos(270+23)
= cos5 + cos77 - sin59 - cos41 + sin23
= cos5 + cos77 - cos31 - cos41 + cos67
= (cos5 + cos77) - (cos31 - cos67) - cos 41
= 2.cos41.cos36 - 2.sin49.sin18 - cos41
= 2.cos41.cos36 - 2.cos41.sin18 - cos41
= 2.cos41(cos36 - sin18) - cos41
= 2.cos41{(√5+1)/4 - (√5-1)/4} - cos41
= cos41 - cos41
= 0 (Answer)
1there is no need to write the answer again and again.if u got right don't mention it again and again
