1.

If Sin D = 3/5, then (sin D + cos D)2 =?A. 1B. 24/25C. 49/25D. 12/251. A2. B3. D4. C

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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