Question

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

Answer 1

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

Answer 2

Hello here is a solution :