Question

Question! sin²5 + sin²10 + sin²15 +.... + sin²85° + sin²(90°) =?



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Answer 1

Answer:

sin θ = cos (90° – θ);

sin (90° – θ) = cos θ

∴ sin 85° = sin (90° – 5°) = cos 5°

∴ (sin² 5° + sin² 85°) + (sin² 10° + sin² 80°) + ... to 8 terms + sin² 45° + sin² 90°

$8 \times 1 + \frac{1}{2} + 1 = 9 \frac{1}{2}$

Answer 2

⇢Question:-

• sin²5 + sin²10 + sin²15 + ••• + sin²85° + sin²(90°) =?

⚘Answer:-

• $\huge\mathfrak\red{9 \frac{1}{2} }$

⚘Explanation:-

ㅤㅤㅤ⇢ sin θ = cos (90° – θ)

ㅤㅤㅤ⇢ sin (90° – θ) = cos θ

ㅤㅤㅤㅤ∴ sin 85° = sin (90° – 5°) = cos 5°

ㅤㅤㅤㅤ∴ (sin² 5° + sin² 85°) + (sin² 10° + sin² 80°) + •••• ㅤㅤㅤㅤㅤto 8 terms + sin² 45° + sin² 90°

$= \small\mathfrak\red{8 \times 1 + \frac{1}{2} + 1}$

$= \small\mathfrak\green{9 \frac{1}{2} }$

ㅤ⚘⇢ So, your answer was 9 whole 1/2