Is 5cos^2(θ)+3sin^2(θ)=3+2cos^2(θ) ?

The answer to whether 5cos^2(θ)+3sin^2(θ)=3+2cos^2(θ) is True

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prove 5cos^2(θ)+3sin^2(θ)=3+2cos^2(θ)

prove

5 cos^{2} (θ) + 3 sin^{2} (θ) = 3 + 2 cos^{2} (θ)

True

Solution steps

5 cos^{2} (θ) + 3 sin^{2} (θ) = 3 + 2 cos^{2} (θ)

Manipulating left side

5 cos^{2} (θ) + 3 sin^{2} (θ)

Rewrite using trig identities

= 2 cos^{2} (θ) + 3

= 3 + 2 cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (x + \frac{π}{3}) + cos (x - \frac{π}{3}) = cos (x)

3 cos (x + y) + 3 cos (x - y) = 6 cos (x) cos (y)

cos (x) = 2 cos^{2} (\frac{x}{2}) - 1

tan (x + \frac{π}{4}) = \frac{tan ( x ) + 1}{1 - tan ( x )}

csc (θ) cos (θ) tan (θ) = 1

Is 5cos^2(θ)+3sin^2(θ)=3+2cos^2(θ) ?
The answer to whether 5cos^2(θ)+3sin^2(θ)=3+2cos^2(θ) is True