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use the fundamental identities to fully simplify the expression

3sin^3 x csc x + cos^2 x + 2 cos(-x) cos x


I simplified it until this

3sin^2 x + cos^2 x +2cos^2(-x)*cos(x)


I know the answer is suppose to be 3 but I don't know how to simplify further to get to 3

Verified Answer :

ghanami

Hello here is a solution :

View image ghanami
thewisestudent9

Hey!

Hope this helps... And we're super sorry that no answered your question...

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3sin^3 x csc(x) + cos^2 x + 2cos(-x) cos(x) = ?

3sin^3 x (1/sin) + cos^2 x + 2cos(x) cos(x) = ? We know 2cos(-x) = 2cos(x) because of the opposite angle theorem: cos(-x) = cos(x)

3sin^2 x + cos^2 x + 2cos(x) cos(x) = ?

3sin^2 x + cos^2 x + 2cos^2 x = ?

sin^2 x + cos^2 x + 2cos^2 x = ?

3sin^2 x + 3cos^2 x = ?

3 (sin^2 x + cos^2 x) = ?

3 1 = ?

= 3

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