how 2sinthetacostheta=sin2thetaexplain the above question

2 Answers

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You may solve the problem either transforming the product`sin theta*cos theta`  into a sum of two like trigonometric function or writing the double of the angle `theta`  as the sum `theta + theta` .

I'll focus on the first solving strategy such that:

`sin theta*cos theta = (1/2)[sin(theta - theta) + sin (theta + theta)]`

`sin theta*cos theta = (1/2)[sin(0) + sin (2theta)]`

Since sin 0 = 0 => `2sin theta*cos theta = sin (2theta)`

This last line proves the given identity.

beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

the sine addition formula is

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

if A = B then

sin(A+A) = sin(A)cos(A) + sin(A)cos(A)

this simplifies to

sin(2A) = 2 sin(A)cos(A)  which proves your question.