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For all i's, i = 1, 2, 3, …, 20 lying between 0° and 90°, it is given that, sin ∝1 + sin ∝2 + sin ∝3 ………. + sin ∝20 = 20 What is the value (in degrees) of (∝1 + ∝2 + ∝3 + … … + ∝20)?

For all i's, i = 1, 2, 3, …, 20 lying between 0° and 90°, it is given that, sin ∝1 + sin ∝2 + sin ∝3 ………. + sin ∝20 = 20 What is the value (in degrees) of (∝1 + ∝2 + ∝3 + … … + ∝20)? Correct Answer 1800

The maximum value of sin α is 1.

⇒ α = 90°

⇒ sin ∝1 + sin ∝2 + sin ∝3 ………. + sin ∝20 = 1 + 1 + 1 + ... up to 20 terms

⇒ sin ∝1 + sin ∝2 + sin ∝3 ………. + sin ∝20 = sin 90° + sin90° + ... up to 20 terms

⇒ ∝1 = ∝2 = ∝3 = ... = ∝20 = 90°

⇒ (∝1 + ∝2 + ∝3 + … … + ∝20) = 90° + 90° + ... up to 20 terms

⇒ (∝1 + ∝2 + ∝3 + … … + ∝20) = 90° × 20 = 1800°

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