How do you find the value of #cos30# using the half angle identity?

Question

5810 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-24T07:27:51

#cos30^@=sqrt3/2#

We use the half angle identity #cosA=2cos^2(A/2)-1#

Let #A/2=30^@# Hence #2A=60^@#

and hence from the above identity we get

#cos60^@=2cos^2 30^@-1#

or #1/2=2cos^2 30^@-1#

or #2cos^2 30^@=1+1/2=3/2#

Hence #cos^2 30^@=3/4#

and #cos30^@=sqrt3/2#

Note we cannot have #cos30^@# as #-sqrt3/2#, as cosine of an angle in #Q1# cannot be negative.