Question

Sine²π/18+sin²2π/9+sin²7π/18+sin²4π/9

Answer 1

sin²π/18 + sin²π/9 + sin²7π/18 + sin²4π/9
=sin²10° +sin²20° +sin²70° +sin²80° (applying π=180°)
=[sin(90-80°)]² +[sin(90-70)]² +sin²70° +sin²80°
=cos²80°+cos²70°+sin²70°+sin²80°
=(cos²80°+sin²80°) + (cos²70°+sin²70°)
Using:cos²x+sin²x=1 ,we get —
=1+1
=2
=R.H.S.

Answer 2

$\frac{sin^2 \pi }{18} + \frac{sin^22 \pi }{9} + \frac{sin^27 \pi }{18} +\frac{sin^24 \pi }{9}$

$\frac{(sin \pi )^2}{18} + \frac{(sin2\pi)^2}{9} + \frac{(sin7\pi)^2}{18} +\frac{(sin4\pi)^2}{9}$

$\frac{0^2}{18}+ \frac{0}{9} +\frac{0^2}{18} + \frac{0}{9}$

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