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If Sin D = 3/5, then (sin D + cos D)2 =?A. 1B. 24/25C. 49/25D. 12/251. A2. B3. D4. C |
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Answer» Correct Answer - Option 4 : C Given: Sin D = 3/5, we have to find the value of (sin D + cos D)2 Concept Used: Sinθ = Height/Hypotenuse Cosθ = Base/Hypotenuse In a Right angle triangle, Height2 + Base2 = Hypotenuse Calculation: Sin D = 3/5 = Height/Hypotenuse ⇒ Height = 3k and Hypotenuse = 5k [Where k is a constant] We know, Height2 + Base2 = Hypotenuse ⇒ (3x)2 + Base2 = (5x)2 ⇒ Base2 = 25x2 - 9x2 ⇒ Base2 = 16x2 ⇒ Base = 4x Cos D = 4x/5x ⇒ Cos D = 4/5 (sin D + cos D)2 ⇒ (3/5 + 4/5)2 ⇒ (7/5)2 ⇒ 49/25 ∴ The required value of (sin D + cos D)2 is 49/25. |
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