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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (x) + cot (x) = (sec (x)) (csc (x))

sin (x) + sin (x) tan^{2} (x) = tan (x) sec (x)

sin (θ) (csc (θ) - sin (θ)) = cos^{2} (θ)

sec (y) cos (y) = 1

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

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