Is cos^3(θ)+sin^2(θ)cos(θ)=cos(θ) ?

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

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prove cos^3(θ)+sin^2(θ)cos(θ)=cos(θ)

prove

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

True

Solution steps

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

Manipulating left side

cos^{3} (θ) + sin^{2} (θ) cos (θ)

Factor

cos^{3} (θ) + cos (θ) sin^{2} (θ) : cos (θ) (cos^{2} (θ) + sin^{2} (θ))

= (cos^{2} (θ) + sin^{2} (θ)) cos (θ)

Rewrite using trig identities

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot^{2} (a) = cos^{2} (a) + ((cot (a)) (cos (a)))^{2}

(1 - sin^{2} (t)) (1 + tan^{2} (t)) = 1

1 - cosh^{2} (x) = - sinh^{2} (x)

tan^{2} (x) + sec^{2} (x) = 1 - cos (2 x)

cot^{2} (θ) + 1 = csc^{2} (θ)

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