Question

Sin 10 Sin 30 Sin 50 sin 70 = 1/16

Answer 1

Hey there !!!!!!!!!!!!!!

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sin10sin30sin50sin70

We know that sin(90-x)= cosx

So sin70= sin(90-20) = cos20

= sin10sin30sin50cos20 

Multiplying and dividing with 2cos10

= 2cos10sin10sin30sin50cos20/2cos10

We know that 2sinxcosx=sin2x and sin50=sin(90-40) = cos40

So,

= sin20sin30cos40cos20/2cos10

Multiplying and dividing with "2"

= 2sin20cos20sin30cos40/4cos10

= sin40cos40sin30/4cos10


Multiplying and dividing with "2"

= 2sin40cos40sin30/8cos10

= sin80sin30/8cos10

= cos10/16cos10

= 1/16

LHS=RHS

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Hope this helped you................

Answer 2

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.