Question

cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x equals two times secant of x.

Answer 1

\[\frac{\cos(x)}{1+\sin(x)}+\frac{1+\sin(x)}{\cos(x)}=2\sec(x)?\]

Answer 2

assuming you are trying to show this is an identity
I would first combine the fractions of the left

Answer 3

you know since we want to go from 2 terms to one term

Answer 4

need to make 2 terms one term by combining fractions

Answer 5

rationalise the denominator of first term and proceed.

Answer 6

\[\frac{ \cos x }{ 1+\sin x }\times \frac{ 1-\sin x }{ 1-\sin x }=\frac{ \cos x \left( 1-\sin x \right) }{ 1-\sin x }=?\]

Answer 7

correction denominator
\[=1-\sin ^2x\]