Question

Verify the Identity: cot θ ∙ sec θ = csc θ

Answer 1

@iambatman

Answer 2

re-write in terms of sine and cosine and it should be clear

Answer 3

can someone walk me through it

Answer 4

Like Irish boy said, rewrite them:

\(\Huge \frac{\cos\theta}{\sin\theta}*\frac{1}{\cos\theta}=\frac{1}{\sin\theta} \)

Answer 5

Notice anything that can cancel?

Answer 6

i got 1/tan(θ)*1/cos(θ)=csc(θ)

Answer 7

@lυἶცἶ0210

Answer 8

Why did you rewrite it like that?

Answer 9

i replaced the left side to try to make it equal to the right

Answer 10

Well you're right on that. But changing it to sines and cosines is usually easier.

Answer 11

how do i do that

Answer 12

Well cotanget can be seen as the reciprocal of tanget in terms of sine and cosine.

So when \(\large \tan\theta=\frac{a}{b} \) that means \(\large \cot\theta=\frac{b}{a} \)

So \(\Large tan\theta=\frac{sin\theta}{cos\theta} \) , just reciprocate that \(\Large cot\theta=\frac{cos\theta}{sin\theta} \) like I showed you earier.

Answer 13

You got the \(\sec\theta\) right as \(\large \frac{1}{cos\theta}\)

Answer 14

Just cross-cancel now and the answer will reveal itself

Answer 15

ok thank you

Answer 16

Hmmm, you're welcomee, if you have any more questions don't hesitate to ask! Good luck \(\Huge \color{green}\star^{\color{red}{\star^{\color{blue}{\star}}}} \)

Answer 17

so from cos(θ)/sin(θ)*1/cos(θ)=csc(θ) i cancel cos(θ) with it self @lυἶცἶ0210

Answer 18

@CGGURUMANJUNATH can you help me finish this please lυἶცἶ0210 went offline

Answer 19

@butterflydreamer @Godlovesme @IrishBoy123

Answer 20

irish is that last part i said right is that what i do

Answer 21

butter fly i believe i cancel cos(θ) with its self so my final answer is 1/Sin θ = csc θ

Answer 22

that is correct.