How do you simplify #sin^2theta-2cos(2theta )# using the double angle identities?

1 Answer
Karthik G
Dec 22, 2015

#3 - 5cos^2(theta)#

Explanation:

Since you have to use double angle identities the following can be used.

#cos(2theta) = cos^2(theta) - sin^2(theta)#

The working :

#sin^2(theta) - 2cos(2theta)#
#=sin^2(theta) - 2(cos^2(theta) - sin^2(theta))#
#=sin^2(theta) - 2cos^2(theta) + 2sin^2(theta)#
#=sin^2(theta) + 2sin^2(theta) - 2sin^2(theta)#
#=3sin^2(theta) - 2cos^2(theta)#
#=3(1-cos^2(theta)) - 2cos^2(theta)#
#=3-3cos^2(theta) - 2cos^2(theta)#
#=3 - 5cos^2(theta)# Final answer

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