Question

Which of the following are trigonometric identities?

a. tanx cosx cscx = 1
b. ((secx - cosx)/(secx))= sin^2x
c. 1 - tanx tany = (cos(x+y))/ (cosx cosy)
d. 4cosx sinx = 2cosx + 1 - 2sinx

Answer 1

tanx cosx cscx = 1
(sinx/cosx)cos(x)(1/sinx)=1

cos and sin cancels and you get 1=1

Answer 2

Any others? There is supposed to be more than one answer...

Answer 3

Oh, and thank you for explaining @SolomonZelman.

Answer 4

Anytime

Answer 5

b. ((secx - cosx)/(secx))= sin^2x

secx/secx - cosx/secx = sin^2x
1 - cos^2x = sin^2x

thus this is also an identity

Answer 6

None of the other ones? @SolomonZelman

Answer 7

No, I don't think so. You might want to still check them.

Answer 8

I'm not sure how to. I have a formula sheet here, but I'm not sure how to use it @SolomonZelman

Answer 9

what is tanx ± tany ?

I think it might be that one side of choice d is nominator and the other is the denominator
or the other way.

Answer 10

Huh?

Answer 11

I can't work all of them out like that. It's too much.

Answer 12

I have never learned about \[tanx \pm tany\]...

Answer 13

I mean tanx + tany and tanx - tany

Answer 14

I know, but I didn't know that tan could have both an x and a y.

Answer 15

We know this cos(x + y) = cosxcosy - sinxsiny
=> cosxcosy - sinxsiny / cosxcosy
= cosxcosy/cosxcosy - sinxsiny/cosxcosy
= 1 - tanxtany

hence C is an identitity

Answer 16

4cosx sinx = 2cosx + 1 - 2sinx=0
4cos(x)sin(x)-2cos(x)+2sin(x)=0
(2sinx-1)(2cosx+1)=0

2sinx-1=0, sinx=1/2 2cosx+1=0, cosx= -1/2

Answer 17

It's not an identity...

Answer 18

Ok, thank you so much!

Answer 19

Are you sure that b is an identity?

Answer 20

yes