Question

: Is $ \sin 2x $ same as $ 2\sin x $ ?

Answer 1

Hint: Here we are given two trigonometric functions and we have to check whether they are the same or not. Observe the two given functions and then find whether they are the same means of equivalent value or not.

Complete step by step solution:
Trigonometric functions are the real functions which relate an angle of the right angled triangle with the ratios of any two sides of the triangle.
Sine function can be defined as the ratio of the opposite side with the hypotenuse.
From the given statement we observe that we are given two sine functions that is –
 $ \sin 2x $ and $ 2\sin x $
In any trigonometric function, there are two parts: first part function and second function is the angle of measure. Here we are given an angle in terms of the variable “x”.
Taking all together both the parts of the trigonometric functions both the angles are different since and “x” differs but the ratio of two again the angle when goes with the function it gives the resultant value.
We also have trigonometric identity such as-
 $ \sin 2x = 2\sin x\cos x $
Hence, $ \sin 2x $ and $ 2\sin x $ are not the same.

Note: Always remember the basic trigonometric identities for the accurate and an efficient solution. know the correlation between them as sine and cosec are inverse functions of each other. Also, remember that the most important property of sines and cosines is that their values lie between minus one and plus one. Every point on the circle is unit circle from the origin. So, the coordinates of any point are within one of zero as well.
Directly the Pythagoras identity are followed by sines and cosines which concludes that – $ {\operatorname{Sin} ^2}\theta + {\operatorname{Cos} ^2}\theta = 1 $