For all i's, i = 1, 2, 3, …, 20 lying between 0° and 90°, it is given that, sin α1 + sin α2 + sin α3 ………. + sin α20 = 20. What is the value (in degrees) of (α1 + α2 + α3 ………. + α20 )?
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 1800
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Concept |
Application |
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Maximum value of sin α is 1. |
sin α1 + sin α2 + sin α3 ………. + sin α20 = 20 Putting α1 = α2 = α3 = ……… = α20 sin α + sin α + sin α ………. + sin α = 1 + 1 + 1 + …... up to 20 terms ⇒ sin α + sin α + sin α ………. + sin α = sin 90° + sin90° + …... up to 20 terms Hence, α = 90° ⇒ (α + α + α + … … + α) = 90° + 90° + ... up to 20 terms ⇒ (α + α + α + … … + α) = 90° × 20 = 1800° |