These formulas can be derived using x + y formulas

###
**
For sin 2x
**

sin 2x = sin (x + x)

*
Using
*
*
sin (x + y) = sin x cos y + cos x sin y
*

= sin x cos x + sin x cos x

= 2 sin x cos x

###
**
For cos 2x
**

cos 2x = cos (x + x)

*
Using cos
*
*
(x + y) = cos x cos y – sin x sin y
*

= cos x cos x – sin x sin x

= cos
^{
2
}
x – sin
^{
2
}
x

*
Putting cos
*
^{
2
}
*
x = 1 – sin
*
^{
2
}
*
x
*

cos 2x = cos
^{
2
}
x – sin
^{
2
}
x

= 1 – sin
^{
2
}
x – sin
^{
2
}
x

= 1 – 2sin
^{
2
}
x

*
Putting sin
*
^{
2
}
*
x = 1 –
*
*
cos
*
^{
2
}
*
x
*

cos 2x = cos
^{
2
}
x – sin
^{
2
}
x

= cos
^{
2
}
x – (1 – cos
^{
2
}
x)

= cos
^{
2
}
x – 1 + cos
^{
2
}
x

= 2cos
^{
2
}
x – 1

###
**
For tan 2x
**

**
**