Question

Trig question please help asap! Fan and medal! :)
Simplify the trigonometric expression.
cos^2 (theta)
-----------
1 - sin (theta)
A. sin (theta)
B. 1 + sin (theta)
C. 1 - sin (theta)
D. 1 - sin (theta)/sin (theta)

Answer 1

what's another way of writing \[\cos ^{2}\theta\]

Answer 2

cos * cos (theta)?

Answer 3

@alekos

Answer 4

no. use \[\sin ^{2}\theta + \cos ^{2}\theta = 1\]

Answer 5

so \[\cos ^{2}\theta = ?\]

Answer 6

1 - sin^2 (theta)?

Answer 7

yes thats it, so we now have

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

Answer 8

can you see what we need to do next?

Answer 9

so it would be A?

Answer 10

no not at all

Answer 11

the numerator can be expressed as the product of two factors

Answer 12

oh oops

Answer 13

any ideas?

Answer 14

I'm thinking that it's either C or D

Answer 15

you're just guessing and not answering my question

Answer 16

i'm going

Answer 17

i'm going with my gut is what i'm doing.

Answer 18

why are you going?

Answer 19

thats not how you do maths

Answer 20

product of two factors. what do you think?

Answer 21

Don't go off in a frenzy if I get it wrong but would it (the numerator) be (1 - sin)(sin (theta))?

Answer 22

you're a funny girl. let x = sin(theta)

so we have 1 - x^2

Answer 23

and 1 - x^2 = (1-x)(1+x)

Answer 24

i'm just doing the numerator only

Answer 25

do you follow?

Answer 26

yes so far

Answer 27

so the numerator is (1-x)(1+x)

and the denominator is 1-x

Answer 28

what can we do now?

Answer 29

so written all out (what you just wrote, just to clarify) it would look like {(1-x)(1+x)}/(1-x)? would the 1-x cancel out?

Answer 30

excellent thats right!

Answer 31

and we have 1+x
substitute back x = sin(theta)

Answer 32

and the answer is?

Answer 33

B

Answer 34

well done. I hope you now understand how its done?

Answer 35

yes much better :) ty!!!!!!!!!!!!!

Answer 36

your welcome