I can't remember what formula to use for these.

Note- the X's may be replaced by a theta symbol. I just didn't have one on my keyboard.
Use the given information to find sin2X, cos2X and tan2X if 0< X <pi/2

1. sinX=12/13

2. cosX=3/5

3. tanX=2/3

You use the double angle formulas.

To type θ, you need to type the following without the double quotes nor the spaces: "& t h e t a ;".

As Diana suggested, use the double angle formulas. I'll do the first one as an example.
sin(2θ)
=2sin(θ)cos(θ)
sin(&theta)=12/13
cos(&theta)=sqrt(1²-(12/13)²)=5/13
Therefore
sin(2θ)
=2sin(θ)cos(θ)
=2(12/13)(5/13)
=120/169

To find the values of sin2X, cos2X, and tan2X, we can use the double-angle formulas for trigonometric functions. These formulas relate the values of trigonometric functions of an angle to the values of trigonometric functions of twice that angle.

1. Given sinX = 12/13, we can find sin2X using the formula:
sin2X = 2 * sinX * cosX
Substituting the value of sinX (12/13) and cosX (from part 2), we get:
sin2X = 2 * (12/13) * (3/5)
Simplifying the expression, we find:
sin2X = 72/65

2. Given cosX = 3/5, we can find cos2X using the formula:
cos2X = cos^2(X) - sin^2(X)
Substituting the value of cosX (3/5) and sinX (from part 1), we get:
cos2X = (3/5)^2 - (12/13)^2
Simplifying the expression, we find:
cos2X = 9/25 - 144/169
To subtract two fractions, we need a common denominator. The least common multiple of 25 and 169 is 4225.
cos2X = (9/25)*(169/169) - (144/169)*(25/25)
Simplifying further:
cos2X = 1521/4225 - 3600/4225
cos2X = -2079/4225

3. Given tanX = 2/3, we can find tan2X using the formula:
tan2X = (2 * tanX) / (1 - tan^2(X))
Substituting the value of tanX (2/3) into the formula, we get:
tan2X = (2 * (2/3)) / (1 - (2/3)^2)
Simplifying the expression, we find:
tan2X = (4/3) / (1 - 4/9)
tan2X = (4/3) / (5/9)
To divide by a fraction, we can multiply by its reciprocal:
tan2X = (4/3) * (9/5)
tan2X = 36/15
Simplifying the fraction, we have:
tan2X = 12/5

So, the values of sin2X, cos2X, and tan2X are:
sin2X = 72/65
cos2X = -2079/4225
tan2X = 12/5