Is cos^3(θ)+cos(θ)sin^2(θ)=cos(θ) ?

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

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prove cos^3(θ)+cos(θ)sin^2(θ)=cos(θ)

prove

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

True

Solution steps

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

Manipulating left side

cos^{3} (θ) + cos (θ) sin^{2} (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

csc (θ) sin (θ) = 1

(1 - cos (x))^{2} = csc^{2} (x) - 2 cot (x)

cos^{2} (9 x) - sin^{2} (9 x) = cos (18 x)

1 + cot^{2} (3 0^{\circ}) = csc^{2} (3 0^{\circ})

\frac{1}{1 + tan ^{2} ( θ )} = cos^{2} (θ)

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