Question

rewrite terms in sine and cosine only:

sec X - cosX/(1+sin X)

Answer 1

we can substitute this:
\[\sec x = \frac{1}{{\cos x}}\]

Answer 2

so we can write:
\[\sec x - \frac{{\cos x}}{{1 + \sin x}} = \frac{1}{{\cos x}} - \frac{{\cos x}}{{1 + \sin x}}\]

Answer 3

how would i simplify it?

Answer 4

hint:
the common denominator is:
\[\cos x\left( {1 + \sin x} \right)\]

Answer 5

what is:
\[\frac{{\cos x\left( {1 + \sin x} \right)}}{{\cos x}} = ...?\]

Answer 6

how is cos the denominator?

Answer 7

it is an intermediate step

Answer 8

the denominator of our new equivalent fraction is:
\[{\cos x\left( {1 + \sin x} \right)}\]

Answer 9

then i get \[\frac{1+\sin X-\cos ^{2}X\ }{ cosX(1+sinX) }\]

Answer 10

correct!

Answer 11

now, we can use this identity:
\[{\left( {\cos x} \right)^2} = \left( {1 - \sin x} \right)\left( {1 + \sin x} \right)\]

Answer 12

oh yay thank you so much !!!

Answer 13

:)