Question

Trig/ Pre Cal/identies Am I on the right path?

Please do not give answer but guide me. Thank you.

The problem
\[ \frac{1}{\sin x + 1} + \frac{1}{\csc x +1} \]
\[ \frac{\csc x + 1 + \sin x + 1}{( \sin x + 1)( \csc x + 1)}\]

Am I on the right path?

Answer 1

it should be
\[ \frac{1}{\sin x + 1} + \frac{1}{\csc x +1} = 1 \]
\[ \frac{\csc x + 1 + \sin x + 1}{( \sin x + 1)( \csc x + 1)} = 1\]

Answer 2

well first write csc in terms of sin :-) that will be easy :-)

Answer 3

\[ \frac{1}{\sin x + 1} + \frac{1}{\rm \color{reD}{\frac{1}{sinx} +1}} = 1 \]
like this solve red part first

Answer 4

So



\[ \frac{\frac{1}{sin x} x + 1 + \sin x + 1}{( \sin x + 1)( \frac{1}{sin x} x + 1)}\]

Answer 5

better to gget rid of fraction first :-)

Answer 6

so do I times the numerator and denominator by sin??

Answer 7

\[ \frac{1}{\sin x + 1} + \frac{1}{\rm \color{reD}{\frac{1}{sinx} +1}} = 1 \]
\[\large\rm \color{reD}{\frac{ 1 }{ \sin x } +1}\]
multiply by sinx/1
do you know how to find common denominator ?
just for the red part

Answer 8

For the red part the common denominator is sin x and 1. For the red we have
\[ 1+ \sin x \] corect?

Answer 9

for the red part
common denominator is sin x