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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( x )}{sec ( x ) - tan ( x )}

Express with sin, cos

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

Rewrite using trig identities

= sin (x) + 1

= 1 + sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

2 csc (2 x) = csc^{2} (x) tan (x)

\frac{sec ^{2} ( t )}{tan ( t )} = cot (t) + tan (t)

csc (\frac{π}{2} - x) = sec (x)

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

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