Question

I need help prooving a trigometric equation

Answer 1

What is it?

Answer 2

1/tanx=cotx/sin^2x+cos^2x

Answer 3

Hint ; sin^2x+cos^2x = 1

Answer 4

my teacher wants me to provide proofs for the lhs and rhs and provide reasons but I am so clueless

Answer 5

First, you can write the left side as cosx/sinx since the reciprical of tanx, or 1/tanx, is cosx/sinx.

Answer 6

so they both mean the same thing?

Answer 7

Yes.

Answer 8

And as @cwrw238 said, sin^2x+cos^2x=1, so the left side becomes cotx, which is cosx/sinx.
Because the right side and left side are same, it is proven.

Answer 9

okay thanks! that makes some sense, but im still confused as to what the reason are..

Answer 10

Let's start with the left side reasoning.

Answer 11

Do you understand that tanx=sinx/cosx?

Answer 12

yes and that equals 1

Answer 13

but its one over tanx

Answer 14

So, the reciprical of tanx is the reciprical of sinx/cosx, which is cosx/sinx. Right?

Answer 15

ok right

Answer 16

Now, moving on to the right side.

Answer 17

Do you understand that sin^2x+cos^2x=1?

Answer 18

yes

Answer 19

So, the denominator becomes 1.

Answer 20

okay what about the numerator

Answer 21

The numerator is cotx,which can be written as cosx/sinx, right?

Answer 22

right

Answer 23

Now, we just proved that left side is cosx/sinx, and same with the right side.

Answer 24

okay thank you so much! I have so many other equations to proof though