sin10° sin30° sin50° sin70°
⇒ 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.
⇒ 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.
^_^
:)
Answers
Answered by
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We have sinx*sin(60 – x)*sin(60 + x) = 1/4* sin3x
sin10*sin30*sin50*sin70
=1/2*sin10*sin(60 – 10)*sin(60 + 10)
=1/2*1/4*sin(3*10)
=1/2*1/4*1/2
=1/16
OR
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.
Similar questions
⇒ (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