Is cos^2(θ)+tan^2(θ)cos^2(θ)=1 ?

The answer to whether cos^2(θ)+tan^2(θ)cos^2(θ)=1 is True

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prove cos^2(θ)+tan^2(θ)cos^2(θ)=1

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (θ) + tan^{2} (θ) cos^{2} (θ)

Express with sin, cos

= cos^{2} (θ) + sin^{2} (θ)

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

1 - cos (x) = sin (x)

csc (x) - sin (x) = cot (x) \cdot cos (x)

sin^{4} (y) - cos^{4} (y) = 1 - 2 cos^{2} (y)

1 - sin^{2} (- θ) = cos^{2} (θ)

tan (θ) csc^{2} (θ) - tan (θ) = cot (θ)

Is cos^2(θ)+tan^2(θ)cos^2(θ)=1 ?
The answer to whether cos^2(θ)+tan^2(θ)cos^2(θ)=1 is True