Question

Somebody help! Will FAN and MEDAL
Simplify the trig expression

Answer 1

@jim_thompson5910

Answer 2

@satellite73

Answer 3

Start off with the idea that

cos^2 + sin^2 = 1

Answer 4

what is cos^2 in terms of sin?

Answer 5

Hmm, like the reciprocal identity?

Answer 6

how would you isolate cos^2

Answer 7

in the equation cos^2 + sin^2 = 1

Answer 8

cos^2= sin^2 + 1 ?

Answer 9

close but no

Answer 10

is it minus one?

Answer 11

cos^2 = 1 - sin^2

Answer 12

Ohh

Answer 13

Thats one of the indentities

Answer 14

yes, the pythagorean identity

Answer 15

so that would mean cos^2 is equal to 1

Answer 16

no

Answer 17

Oh okay, I'm lost again then

Answer 18

do you see how cos^2 + sin^2 = 1

Answer 19

yes

Answer 20

do you see how I'm getting cos^2 = 1 - sin^2

Answer 21

yes

Answer 22

So...

\[\Large \frac{\cos^2(\theta)}{1 - \sin(\theta)}\]

\[\Large \frac{1-\sin^2(\theta)}{1 - \sin(\theta)}\]

what's next?

Answer 23

Simplify by canceling out?

Answer 24

that comes later

Answer 25

I'm not sure then

Answer 26

factor the numerator

Answer 27

Like (sin) (sin)?

Answer 28

kinda

Answer 29

you'd use the difference of squares rule

Answer 30

Okay I factored it, well I tried anyway.. is it 1-sin?

Answer 31

check out this

http://www.purplemath.com/modules/specfact.htm

Answer 32

(1-csc)(1+csc) ?

Answer 33

closer but no

Answer 34

Or am I just not getting this at all?

Answer 35

Aw poop, okay hold on

Answer 36

Actually, never mind, I don't think I am getting it

Answer 37

use

a^2 - b^2 = (a-b)(a+b)

Answer 38

a = 1
b = sin(theta)

Answer 39

(1-sin)(1+sin) ?

Answer 40

yep

Answer 41

YES

Answer 42

you'll notice something cancelling

Answer 43

Okay, I should get 1+sin

Answer 44

yep

Answer 45

Thank you so much! (: