Question

Verify the identity.

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

\[\frac{ cosx }{ 1+sinx } + \frac{ 1+sinx }{ cosx } = 2secx\]

Answer 2

sec = 1/cos

Answer 3

multiply everything everything by cos x

Answer 4

cos^2x = 1-sin^2x = 1+sinx)(1- sinx) so u have 1+sin x left in 1 term on left

Answer 5

and 1+ sin x left

Answer 6

there for 1-sinx+1+sinx =2 yes true

Answer 7

therefore*

Answer 8

make sense?

Answer 9

Partially, from my experience in this shouldn't you first make the denominators common to one another. My teacher taught me to work with the left side first to make sure that it equals the right side to verify it.