sin²pie/10+sin²4pie/10+sin²6pie/10+sin²9pie/10
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Answer:
= \sin^{2} ( \frac{\pi}{10} ) + \sin^{2} ( \frac{4\pi}{10} ) + \sin^{2} ( \frac{6\pi}{10} ) + \sin^{2} ( \frac{9\pi}{10}=sin
2
(
10
π
)+sin
2
(
10
4π
)+sin
2
(
10
6π
)+sin
2
(
10
9π
= \sin^{2} 18 + \sin^{2}72 + \sin^{2}108 + \sin^{2}162=sin
2
18+sin
2
72+sin
2
108+sin
2
162
= \sin^{2}18 + \cos^{2}18 + \sin^{2}72 + \cos^{2}72=sin
2
18+cos
2
18+sin
2
72+cos
2
72
= 1 + 1=1+1
= 2=2
Hope this is helpful
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