Math, asked by chandanpuhan31, 6 months ago

The value of sin 10° x sin 30° x sin 50°x
sin 70° is equal to​

Answers

Answered by madhavsahoo05
0

ANSWER:-

sin10°=sin(90–80)°=cos80°sin⁡10°=sin⁡(90–80)°=cos⁡80°

sin50°=sin(90–40)°=cos40°sin⁡50°=sin⁡(90–40)°=cos⁡40°

sin70°=sin(90–20)°=cos20°sin⁡70°=sin⁡(90–20)°=cos⁡20°

∴sin10°sin30°sin50°sin70°=cos80°sin30°=12cos40°cos20°∴sin⁡10°sin⁡30°sin⁡50°sin⁡70°=cos⁡80°sin⁡30°⏟=12cos⁡40°cos⁡20°

=12⋅cos20°cos40°cos80°=14sin20°⋅(2sin20°cos20°)cos40°cos80°=12⋅cos⁡20°cos⁡40°cos⁡80°=14sin⁡20°⋅(2sin⁡20°cos⁡20°)cos⁡40°cos⁡80°

=18sin20°⋅(2sin40°cos40°)cos80°=18sin⁡20°⋅(2sin⁡40°cos⁡40°)cos⁡80°

=116sin20°⋅(2sin80°cos80°)=116sin⁡20°⋅(2sin⁡80°cos⁡80°)

=116sin20°⋅(sin160°)=116sin20°⋅(sin(180−20°))=116sin⁡20°⋅(sin⁡160°)=116sin⁡20°⋅(sin⁡(180−20°))

=116sin20°⋅sin20°=116=116sin⁡20°⋅sin⁡20°=1/16

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