# I need help proving two Trig identities! (1 Viewer)

### Users Who Are Viewing This Thread (Users: 0, Guests: 1)

#### xxiangel

1. Cos x (sec x + cos x csc^2 x) = csc^2 x

I got as far as this.... 1 + cos^2 + cos/sin^2 = csc^2

2. tan x(sin x + cot x cos x) = sec x

#### moose

1. Change everything on the left into terms of cos and sin. Then distribute the cosx, after that try to combine anything you can, change anything you can to tanx, etc.

2. Again, change everything you can into sin and cos first, then distribute.

A few of the most important things to keep in mind are, when you are done with simplifying things and whatnot, if something is a fraction, combine the terms. In such trig identities, one of the most used basic definitions is tanx=sinx/cosx

Last edited:

#### 0rthodontist

xxiangel said:
I got as far as this.... 1 + cos^2 + cos/sin^2 = csc^2
Well, you made a mistake somewhere. Substitute in some random angle and you can see that this is not true.

#### mrtkawa

hey you, i got this
cosX(secX+cosXcsc^2X)=csc^2x
just solve the left side
cosX[(1/cosX)+(cosx/sin^2X)]=csc^2X
then multiply ,so...
cosX(1/cosX)+cosX(cosX/sin^2X)=csc^2X
1+cot^2X=csc^2X
since 1+cot^2X one of the trig identity which equals
to csc^2X, problem solved

#### z-component

For the future, mrtkawa, have the original poster attempt his/her own work instead of providing the full solution.

#### konartist

I was able to solve this till 1+cot^2 = Csc^2 , but do you just use pythagorean identity to fine the identity or what? How are these two equal?

#### konartist

for 2.

change everything to cos and sin

SinX/CosX[SinX + CosX/SinX(CosX)] = 1/Cosx

work inside the bracket now.

Cosx/sinx(cosx) = cos^2x/sinx
SinX + Cos^2x/Sinx Now get common denominators
you should notice something and be able to work from there.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving