Question

[tex] Show that sin2
18 + sin2
9
+ sin2 7
18 + sin2 4
9 = 2[/tex]
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Answer 1

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★ Wᴇ Nᴇᴇᴅ Tᴏ Pʀᴏᴠᴇ :-

• sin²(π/18) + sin²(π/9) + sin²(7π/18) + sin²(4π/9) = 2

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★ Sᴏʟᴜᴛɪᴏɴ :-

Taking LHS from the question

➥ sin²(π/18) + sin²(π/9) + sin²(7π/18) + sin²(4π/9)

As we know that

π = 180°

Substituting we have

➥ sin²(180°/18) + sin²(180°/9) + sin²[7(180°)/18] + sin²[4(180°)/9]

➥ sin²10° + sin²20° + sin²70° + sin²80°

➥ (0.17)² + (0.34)² + (0.73)² + (1)²

➥ 0.028 + 0.115 + 0.532 + 1

➥ 2.035 ≈ 2

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Hence , proved !

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