Is sec(t)-(cos(t))/(1+sin(t))=tan(t) ?

The answer to whether sec(t)-(cos(t))/(1+sin(t))=tan(t) is True

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prove sec(t)-(cos(t))/(1+sin(t))=tan(t)

prove

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

True

Solution steps

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

Manipulating left side

sec (t) - \frac{cos ( t )}{1 + sin ( t )}

Express with sin, cos

= \frac{1 - cos ^{2} ( t ) + sin ( t )}{( 1 + sin ( t ) ) cos ( t )}

Rewrite using trig identities

= \frac{sin ( t )}{cos ( t )}

Use the basic trigonometric identity:

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

= tan (t)

We showed that the two sides could take the same form

\Rightarrow True

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

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)

Is sec(t)-(cos(t))/(1+sin(t))=tan(t) ?
The answer to whether sec(t)-(cos(t))/(1+sin(t))=tan(t) is True