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DSSSB TGT Maths Male Subject Concerned - 23 Sep 2018 Shift 2

Option 4 : 2

**Concept:**

To find the highest point on the given graph from x-axis, we have to find the the** maximum value of the y component** regarding to maximum value of the x component.

**And,**

**sin(A + B) = sin A.cos B + cos A.sin B**

**Given:**

y = √3 cos x + sin x

Calculation:

On **dividing and multiplying by 2**, we get,

⇒ y = 2.((√3/2) cos x + (1/2) sin x) (∵ sin 60° = √3/2 and cos 60° = 1/2)

⇒ y = 2.(sin 60° cos x + cos 60° sin x)

⇒ y = 2.sin (x + 60°) (∵ sin(A + B) = sin A.cos B + cos A.sin B)

∵ The **maximum value** of sin (x + 60°) is 1.

**⇒ y _{max} = 2×1**

**Hence, **

**The distance of the highest point on the graph of the function y = √3 cos x + sin x from the x-axis is 2.**