34
The value of sin21° + sin2 5° + sin2 9° + ……… + sin2 89° is
- A23/2
- B11 + √2
- C11√2
- D$\frac{{11}}{{\sqrt 2 }}$
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
We know that sin θ = cos(90 - θ). Hence we have
sin 1° = cos 89°
sin 5° = cos 85°
……
Sin 45° = cos 45°
Therefore, we have
cos289° + cos2 85° + cos2 81° + ……… + sin2 89°
We know that sin2θ + cos2θ = 1
Hence,
cos289° + cos2 85° + cos2 81° + ……… + sin2 89° = 1 + 1 + 1….11 times + 1/2 = 23/2
sin 1° = cos 89°
sin 5° = cos 85°
……
Sin 45° = cos 45°
Therefore, we have
cos289° + cos2 85° + cos2 81° + ……… + sin2 89°
We know that sin2θ + cos2θ = 1
Hence,
cos289° + cos2 85° + cos2 81° + ……… + sin2 89° = 1 + 1 + 1….11 times + 1/2 = 23/2