Question

sin2x is.............................. .

Answer 1

Answer:-

sin(2x)=2∗sin(x)∗cos(x)  

It is also

sin(2x)=2∗tan(x)1+tan2(x)

The first proof goes as follows:

Since

sin(a+b)=sin(a)∗cos(b)+cos(a)∗sin(b)

taking a=b

sin(a+a)=sin(a)∗cos(a)+cos(a)∗sin(a)

Therefore,

sin(2x)=2∗sin(x)∗cos(x)

For the second one,

Since sin(2x)=by2∗sin(x)∗cos(x)1

and1=sin2(x)+cos2(x)

sin(2x)=2∗sin(x)∗cos(x)sin2(x)+cos2(x)

Now, lets divide the numerator and the denominator by cos2(x)

sin(2x)=2∗sin(x)/cos(x)sin2(x)/cos2(x)+1

Hence we get

sin(2x)=2∗tan(x)1+tan2(x)