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.



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)


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.

Was this answer helpful?


4.5 (7)


Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published.