Question

Simplify the trig expression. cos(x)(sec(x)-cos(x))

Answer 1

start with \[\cos(x)\left(\frac{1}{\cos(x)}-\cos(x)\right)\]

Answer 2

ok

Answer 3

i still have no idea where to go.

Answer 4

expand the brackets!

Answer 5

use the distributive property to multiply
then use the most famous trig identity of them all

Answer 6

i got 1-cos^2x

Answer 7

do you remember the most famous trig identity?

Answer 8

no

Answer 9

nvm is it sin^2x???

Answer 10

something^2+something^2 = 1

Answer 11

yeah sin^2x+cos^2x=1

Answer 12

cool,

can you rearrange this to be cos^2x = ....

Answer 13

=1-sin^2x

Answer 14

you had
1-cos^2x

now sub in cos^2x = 1-sin^2x

Answer 15

wait what?

Answer 16

im getting sin^2x

Answer 17

Yep, that's right

Answer 18

oh ok cool

Answer 19

what about (tanx+cotx) cotx

Answer 20

use cot = 1 / tan

Answer 21

im actually splittting the expression into 2 fractions. tanx/cotx + cotx/cotx

Answer 22

thats what i did first anyway

Answer 23

then cot over cot is just 1.

Answer 24

so (tanx/cotx)+1

Answer 25

then what u said cot=1/tan... so my result is = tan^2x+1 which is sec^2x

Answer 26

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