Question

1/cot theta + cot theta = csc^2 thetacot theta

Answer 1

\(\Huge\color{blue}{ \sf \frac{1}{cotθ} +cotθ=csc^2θ}\)

are you solving or verifying ?

Answer 2

VERIFYING I THINK

Answer 3

\(\Huge\color{blue}{ \sf \frac{1}{cotθ} +cotθ=csc^2θ}\)

\(\Huge\color{blue}{ \sf \frac{1}{cotθ} + \frac{cot^2θ}{cotθ}=csc^2θ}\)

do you agree with this step?

Answer 4

IDK I DONT GET IT'

Answer 5

I wrote

cot x as cot^2x / cotx

Answer 6

OH OK GOT IT

Answer 7

cot x = cot x / 1 now I am going to multiply top and bottom by cot x and I get,

cot ^2x/cot x

Answer 8

OK,

Answer 9

\(\Huge\color{blue}{ \sf \frac{1}{cotθ} + \frac{cot^2θ}{cotθ}=csc^2θ}\) add the fractions on the left side

\(\Huge\color{blue}{ \sf \frac{1+cot^2θ}{cotθ}=csc^2θ}\)


and we know that

\(\Huge\color{red}{ \sf 1+cot^2θ=csc^2θ}\)

Answer 10

IS THE RED THE ANSWER?

Answer 11

No red is an identity.

Answer 12

So the top of the fraction (on the left side) simplifies to csc^2x

so our next step to simplify the equation would be

\(\Huge\color{blue}{ \sf \frac{csc^2θ}{cot^2θ}=csc^2θ }\)

see how i got this ?

Answer 13

do i write that for the answer?

Answer 14

yes got it

Answer 15

well if you are verifying you would say that it is NOT an identity.

because

\(\Huge\color{blue}{ \sf \frac{csc^2θ}{cot^2θ}≠csc^2θ }\)

Answer 16

but if you are solving for x, you would divide both sides by csc^2θ

\(\Huge\color{blue}{ \sf \frac{csc^2θ}{cot^2θ}=csc^2θ }\)

\(\Huge\color{blue}{ \sf \frac{1}{cot^2θ}=1 }\)

\(\Huge\color{blue}{ \sf tan^2θ=1 }\)

and then you can take it from here to solve for x.

Answer 17

That is if you need to solve. for verifying I already showed you.

Answer 18

sooo what would be the answer for verifying?

Answer 19

for verifying,

NOT AN IDENTITY

Answer 20

yes verifying

Answer 21

i got more problems

Answer 22

(1+ cos theta) (1-cos theta) = sin^2 theta