Double Angle Identities
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Key Questions

#sin2theta=2sin theta cos theta# #cos2theta=cos^2thetasin^2theta=2cos^2theta1=12sin^2theta# #tan2theta={2tan theta}/{1tan^2theta}#
I hope that this was helpful.

Substitute in the one angle you get into the identity.
For example, if you are asked to find
#sin2a# and#a = 30# , then you substitute in#sin2(30) = 2sin30cos30# into your calculator, and that's how you solve equations with double angle identities. 
You can use the double angle ID to evaluate the exact value of a trigonometric expression when you can relate the expression of one of the double angle formulas to one of the special angles.
Ex.1 Evaluate
#2sin(15)cos(15)# using
#sin(2x)=2sinxcosx# , we observe that the left had side of this ID resembles the given question (with#x=15# ).
Thus we can convert the expression to
#2sin(15)cos(15)=sin(2*15)=sin(30)=1/2#
It is also possible to use known values of
#sin(x), cos(x), and tan(x)# to evaluate the exact value of a given trigonometric function of a double angle.Ex.2 Given
#sin(x)=3/5# , find#cos(2x)# To answer this question, we can then use the ID
#cos(2x)=12sin^2(x)# Since
#sin(x)=3/5# , we can find#sin^2(x)=9/25# Therefore
#cos(2x)=12sin^2(x)=12(9/25)=118/25=7/25# 
You would need an expression to work with.
For example:
Given#sinalpha=3/5# and#cosalpha=4/5# , you could find#sin2 alpha# by using the double angle identity
#sin2 alpha=2sin alpha cos alpha# .#sin2 alpha=2(3/5)(4/5)=24/25# .You could find
#cos2 alpha# by using any of:
#cos2 alpha=cos^2 alpha sin^2 alpha#
#cos2 alpha=1 2sin^2 alpha#
#cos2 alpha=2cos^2 alpha 1# In any case, you get
#cos alpha=7/25# .