Question

sin9° + sin18° + sin27° + .... + sin 360°.

Answer 1

Answer:of course the answer will be 1 bcz all the angles gives the sum of 90

Step-by-step explanation:I hope it may help you mark me as brainliest please please please please please

Answer 2

Answer:

The value is $\frac{1}{16}$

Step-by-step explanation:

$\sin \theta=\cos \left(90^{\circ}-\theta\right)$

Now,

$&P=\sin 9^{\circ} \sin 27^{\circ} \sin 63^{\circ} \sin 81^{\circ}$

$&P=\sin 9^{\circ} \sin 27^{\circ} \cos \left(90^{\circ}-63^{\circ}\right) \cos \left(90^{\circ}-81^{\circ}\right)$

$&P=\sin 9^{\circ} \sin 27^{\circ} \cos \left(90^{\circ}-63^{\circ}\right) \cos \left(90^{\circ}-81^{\circ}\right)$

$&P=\frac{1}{4} \sin 18^{\circ} \sin 54^{\circ}$

$&P=\frac{1}{4} \frac{\left(2 \sin 18^{\circ} \cos 18^{\circ}\right) \cos 36^{\circ}}{2 \cos 18^{\circ}}$

$&P=\frac{2 \sin 36^{\circ} \cos 36^{\circ}}{16 \cos 18^{\circ}}$

$&\text { Since, } \cos 18^{\circ}=\sin 72^{\circ}$

$&P=\frac{\sin 72^{\circ}}{16 \cos 18^{\circ}}$

$p=\frac{1}{16}$