Is sec(x)(sec(x)-cos(x))=tan^2(x) ?

The answer to whether sec(x)(sec(x)-cos(x))=tan^2(x) is True

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prove sec(x)(sec(x)-cos(x))=tan^2(x)

prove

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

True

Solution steps

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

Manipulating left side

sec (x) (sec (x) - cos (x))

Expand

(- cos (x) + sec (x)) sec (x) : - sec (x) cos (x) + sec^{2} (x)

= sec^{2} (x) - cos (x) sec (x)

Rewrite using trig identities

= tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( x )} - sin (x) = cot (x) cos (x)

sin (3 x) = 3 sin (x) - 4 (sin (x))^{3}

\frac{sin ( θ ) - 1}{cos ( θ )} = tan (θ) - sec (θ)

cot (x) \cdot sec (x) = csc (x)

2 - csc^{2} (θ) = 1 - cot^{2} (θ)

Is sec(x)(sec(x)-cos(x))=tan^2(x) ?
The answer to whether sec(x)(sec(x)-cos(x))=tan^2(x) is True