Is sin 2x same as 2sinx

Sin 2x is not the same as 2 sin x. Sine of twice of an angle (x) is equal to twice of sine x cos x.  

By trigonometry identities

Sin 2x = 2 Sin x Cos x    ……..(1)

Where x is a reference angle in a right-angled triangle.

 

Therefore, 

2 sin x = (Sin 2x)/(Cos x) ……….(2)

Hence, we can see from the above equation that 2 sin x is not equal to sin 2x.

 

We can also prove it by an example. 

Suppose, if x = π/2, then,

Sin 2x = sin 2(π/2) = sin π = 0      …… (3)

Now,

2sin x = 2 sin (π/2) = 2 (1) = 2   ……… (4)      [sin π/2 = 1] 

From (3) and (4), we get;

Sin 2x ≠ 2sinx

Hence, proved.

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