Grade 12 Trig Question

[JTJ]

I am having trouble with this question. Please show all work:


Determine solutions for:
[cos x / 1+sinx] + [1+sinx / cos x] = 2


On the interval xE[-2pi, 2pi]


See it on paper here:

​< link to objectionable page removed >

I appreciate any help. Thanks!

 

[lookagain]

Determine solutions for: (cos x)/(1+sin x) + (1+sin x)/(cos x) = 2

You must have grouping symbols round appropriate parts of the fractions,
similar to what is shown above when you type it out horizontally.

See it on paper here: <link removed>

The image is blurry/out of focus.

 

[HallsofIvy]

First step (if like me you just don't like fractions) would be to multiply both sides by (1+ sin(x))cos(x).
That gives \(\displaystyle cos^2(x)+ (1+ sin(x))^2= 2cos(x)(1+ sin(x))\)
\(\displaystyle cos^2(x)+ 1+ 2sin(x)+ sin^2(x)= 2cos(x)+ 2sin(x)cos(x)\)
\(\displaystyle 2+ 2sin(x)= 2cos(x)+ 2sin(x)cos(x)\)
\(\displaystyle 1+ sin(x)= cos(x)+ sin(x)cos(x)\)
Can you solve that?