sin 2(3°)+ sin 2(6°)+ sin 2(9°)+ ldots+ sin 2(84°) + sin 2(87°)+ sin 2(90°)=

Question

sin 2(3°)+ sin 2(6°)+ sin 2(9°)+ ldots+ sin 2(84°) + sin 2(87°)+ sin 2(90°)= (A) (31/2) (B) (39/2) (C) (59/2) (D) 36

Tardigrade Admin · Accepted Answer

We have, sin 2(3°)+ sin 2(6°)+ sin 2(9°)+ ldots+ sin 2(84°)+ sin 2(87°)+ sin 2 90° = sin 2(3°)+ sin 2(87°)+ sin 2(6°)+ sin 2(84°)+ ldots sin 2 90° =1+1+1+ ldots 15 times +((1/√2))2=15+(1/2)=(31/2)

Q. $sin^{2} (3^{\circ}) + sin^{2} (6^{\circ}) + sin^{2} (9^{\circ}) + \dots + sin^{2} (8 4^{\circ})$ $+ sin^{2} (8 7^{\circ}) + sin^{2} (9 0^{\circ}) =$

$\frac{31}{2}$

$\frac{39}{2}$

$\frac{59}{2}$

36

Q. sin2(3∘)+sin2(6∘)+sin2(9∘)+…+sin2(84∘) +sin2(87∘)+sin2(90∘)=

231​

239​

259​

36

We have, sin2(3∘)+sin2(6∘)+sin2(9∘)+…+sin2(84∘)+sin2(87∘)+sin290∘ =sin2(3∘)+sin2(87∘)+sin2(6∘)+sin2(84∘)+…sin290∘ =1+1+1+…15 times +(2​1​)2=15+21​=231​

Q. $sin^{2} (3^{\circ}) + sin^{2} (6^{\circ}) + sin^{2} (9^{\circ}) + \dots + sin^{2} (8 4^{\circ})$ $+ sin^{2} (8 7^{\circ}) + sin^{2} (9 0^{\circ}) =$

$\frac{31}{2}$

$\frac{39}{2}$

$\frac{59}{2}$