Is sec(x)-cos(x)=sin(x)*tan(x) ?

The answer to whether sec(x)-cos(x)=sin(x)*tan(x) is True

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prove sec(x)-cos(x)=sin(x)*tan(x)

prove

sec (x) - cos (x) = sin (x) \cdot tan (x)

True

Solution steps

sec (x) - cos (x) = sin (x) tan (x)

Manipulating left side

sec (x) - cos (x)

Express with sin, cos

= \frac{1 - cos ^{2} ( x )}{cos ( x )}

Manipulating right side

sin (x) tan (x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1 - cos ^{2} ( x )}{cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

tan (\frac{x}{2}) = \frac{tan ( x )}{sec ( x ) + 1}

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

2 cos^{2} (\frac{x}{2}) - cos (x) = 1

\frac{tan ( x ) + cot ( x )}{sec ( x )} = csc (x)

sec^{2} (θ) - 1 = tan^{2} (θ)

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