Question

Evaluate: sin^2 10° + sin^2 20° + sin^2 40° + sin^2 50° + sin^2 70° + sin^2 80°
Please answer fast.

Answer 1

Answer :

Now,

sin²10° + sin²20° + sin²40° + sin²50° + sin²70° + sin²80°

= sin²10° + sin²20° + sin²40° + sin²(90° - 40°) + sin²(90° - 20°) + sin²(90° - 10°)

= sin²10° + sin²20° + sin²40° + cos²40° + cos²20° + cos²10°, since sin(90° - θ) = cosθ

= (sin²10° + cos²10°) + (sin²20° + cos²20°) + (sin²40° + cos²40°)

= 1 + 1 + 1, since sin²θ + cos²θ = 1

= 3

#MarkAsBrainliest

Answer 2

[tex]sin^210 + sin^220+ sin^240 + sin^250 + sin^270 + sin^280 \\ \\ \\ sin^2( 90- 80)+ sin^2(90- 70) +sin^2(90 - 50) + sin^250 + sin^270+sin^280 \\ \\ \\ [/tex]

[tex]cos^2 80 + cos^270 + cos^250 + sin^250 + sin^270 + sin^280 \\ \\ \\ \\ cos^280+ sin^280 + cos^270 + sin^270 + cos^250 + sin^250 \\ \\ 1 + 1 + 1 \\ \\ 3 [/tex]



i hope this will help you


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