Is 2cos(θ)-(cos(2θ))/(cos(θ))=sec(θ) ?

The answer to whether 2cos(θ)-(cos(2θ))/(cos(θ))=sec(θ) is True

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prove 2cos(θ)-(cos(2θ))/(cos(θ))=sec(θ)

prove

2 cos (θ) - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

True

Solution steps

2 cos (θ) - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

Manipulating right side

sec (θ)

Express with sin, cos

= \frac{1}{cos ( θ )}

Rewrite using trig identities

= \frac{2 cos ^{2} ( θ ) - cos ( 2 θ )}{cos ( θ )}

Expand

\frac{- cos ( 2 θ ) + 2 cos ^{2} ( θ )}{cos ( θ )} : - \frac{cos ( 2 θ )}{cos ( θ )} + 2 cos (θ)

= - \frac{cos ( 2 θ )}{cos ( θ )} + 2 cos (θ)

= 2 cos (θ) - \frac{cos ( 2 θ )}{cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

cos (2 \cdot 30) = cos^{2} (30) - sin^{2} (30)

1 + tan^{2} (4 5^{\circ}) = sec^{2} (4 5^{\circ})

\frac{cot ( x )}{cos ( x )} = csc (x)

\frac{sin ( x ) cos ( x )}{tan ( x )} = cos^{2} (x)

2 sin^{2} (2 t) + cos (4 t) = 1

Is 2cos(θ)-(cos(2θ))/(cos(θ))=sec(θ) ?
The answer to whether 2cos(θ)-(cos(2θ))/(cos(θ))=sec(θ) is True