Left Side Right Side Proof

[needshelp]

Hey. I was wondering if anyone could help me prove this problem. It is:

sinx + tanx +(cosx)(tanx)= tanx(2cosx +1)

I know you have to use the pythagoream identity and quotient identy, but I am making the two sides equal.

Thanks in advance.

 

[stapel]

sinx + tanx +(cosx)(tanx)= tanx(2cosx +1)

I know you have to use the pythagoream identity and quotient identy, but I am making the two sides equal.

The Pythagorean Identity is, I assume, "sin²(x) + cos²(x) = 1". But what do you mean by "the quotient identity"? And what do you mean by "making the two sides equal"? Are you trying to prove that the posted equation is an identity, or trying to find the value(s) of x that make the two sides equal (that is, solving the equation)?

Thank you.

Eliz.

 

[Unco]

Use tan(x) = sin(x)/cos(x) (the quotient identity, eh?) to simplify cos(x)tan(x) when dealing with each side to show LHS = RHS.

 

[galactus]

\(\displaystyle cosx=\frac{sinx}{tanx}\)

\(\displaystyle sinx+tanx+(\frac{sinx}{tanx})tanx\)

\(\displaystyle sinx+tanx+sinx\)

\(\displaystyle 2sinx+tanx\)

\(\displaystyle sinx=tanxcosx\)

\(\displaystyle 2tanxcosx+tanx\)

factor:

\(\displaystyle tanx(2cosx+1)\)

 

[needshelp]

thanks for the tips. I have it figured out