Question

sin10°sin30°sin50°sin70°=1÷16​

Answer 1

Sol: Given Sin 10 Sin 30 Sin 50 sin 70 ⇒ (1/ 2) Sin 10 Sin 50 sin 70 multiply and divide with 2 Cos 10 ⇒ 2 Cos 10 Sin 10 Sin 50 sin 70 / (2 x 2 Cos 10) { 2SinA Cos A = Sin2A } ⇒ Sin 20 Sin 50 sin 70 / ( 4 Cos 10) multiply and divide with 2 ⇒ 2 x Sin 20 Sin 50 sin (90 - 20) / (2 x 4 Cos 10) ⇒ 2 Sin 20 Cos 20 Sin 50 / 8 Cos 10 ⇒ Sin 40 Sin 50 / 8 Cos 10 { 2SinA Cos A = Sin2A } Again multiply and divide with 2 . ⇒ 2 x Sin 40 Sin ( 90 - 40) / 2 x 8 Cos 10. ⇒ 2 x Sin 40 Cos 40 / 2 x 8 Cos ( 90 - 80) ⇒ Sin 80 / 16 Sin 80 = 1 / 16.

Answer 2

sin10 sin30 sin 50 sin70 = 1/16

=1/2(sin10sin50sin70)

=1/2(sin50 sin70)sin10

​=1/2(sin(60-10)sin(60+10))sin 10

=1/2(sin260-sin210)sin10

​=1/8(3/4-sin210)sin10

=1/8(3-4sin210)sin10

=1/8(3sin10-4sin310)

​=1/8(sin3X10)

=1/16.