Question

find the value of sin10sin20sin30sin40sin50sin60sin70sin80sin90​

Answer 1

The value of :-

sin10=0.1736 (approx).

sin20= 0.34200

sin30= 0.34200

sin40=0.6428 (approx).

sin50=0.766.

sin60= 0.86602540

sin70= 0.865

sin80= 0.98481

sin90=1.

Answer 2

Answer:

The value of $sin10.sin20.sin30.sin40.sin50.sin60.sin70.sin80.sin90$ is $\frac{3}{256}$

Step-by-step explanation:

Given:

$sin10.sin20.sin30.sin40.sin50.sin60.sin70.sin80.sin90$

We need to find the value of this

$=sin10.sin20.sin30.sin40.sin50.sin60.sin70.sin80.sin90\\=sin10.sin20.sin30.sin40.sin(90-40).sin(90-30).sin(90-20).sin(90-10).(1)\\=sin10.sin20.sin30.sin40.cos40.cos30.cos20.cos10\\=\frac{1}{16}*sin20.sin40.sin60.sin80\\= \frac{1}{16}*sin20.sin(60-20).sin(60+20).\frac{\sqrt{3} }{2}$

We know that

$sin\alpha .sin(60-\alpha ).sin(60+\alpha ) =\frac{1}{4}sin3\alpha$

So we get as

$= \frac{1}{16}.\frac{1}{4}sin3(20) .\frac{\sqrt{3} }{2} \\\\=\frac{\sqrt{3} }{128} sin(60)\\\\=\frac{3}{256}$