1. Verifying Identities?

I have two questions that I am getting nowhere on:

1. Verify the identity: cotx+tanx=cscxsecx
I thought of working on the right side, but I came up with (1/tanx)+(sinx/cosx) and didn't know where to go from there.

2. Verify the identity: (15sinx-4cos^2x)/(4+sinx)=4sinx-1
I don't even know where to begin on this one!

Any help is much appreciated, and since I need to show work, a brief explanation is welcomed. Thanks in advance!!

2. Originally Posted by captaintoast87
I have two questions that I am getting nowhere on:

1. Verify the identity: cotx+tanx=cscxsecx
I thought of working on the right side, but I came up with (1/tanx)+(sinx/cosx) and didn't know where to go from there.

2. Verify the identity: (15sinx-4cos^2x)/(4+sinx)=4sinx-1
I don't even know where to begin on this one!

Any help is much appreciated, and since I need to show work, a brief explanation is welcomed. Thanks in advance!!
1. That's because there is nothing more to do, just change them into the LHS using the rules below

$tan(x) = \frac{sin(x)}{cos(x)}$ and $cot(x) = \frac{1}{tan(x)}$

2. $cos^2(x) = 1-sin^2(x)$ so $-4cos^2(x) = -4(1-sin^2(x)) = -4 + 4sin^2(x)$

$
\frac{15sin(x)+4sin^2(x)-4}{4+sin(x)}$

The numerator factorises to $(4sin(x)-1)(sin(x)+4)$

$\frac{(4sin(x)-1)(sin(x)+4)}{sin(x)+4} = 4sin(x)-1$

3. Originally Posted by captaintoast87
I have two questions that I am getting nowhere on:

1. Verify the identity: cotx+tanx=cscxsecx
I thought of working on the right side, but I came up with (1/tanx)+(sinx/cosx) and didn't know where to go from there.

2. Verify the identity: (15sinx-4cos^2x)/(4+sinx)=4sinx-1
I don't even know where to begin on this one!

Any help is much appreciated, and since I need to show work, a brief explanation is welcomed. Thanks in advance!!
Hi captaintoast87,

$\cot x + \tan x = \csc x sec x$

$\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x}=$

$\frac{\cos^2 x+\sin^2 x}{\sin x \cos x}=$

$\frac{1}{\sin x \cos x}=$

$\frac{1}{\sin x} \cdot \frac{1}{\cos x}=$

$\csc x \sec x$

4. Originally Posted by masters
Hi captaintoast87,

$\cot x + \tan x = \csc x sec x$

$\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x}=$

$\frac{\cos^2 x+\sin^2 x}{\sin x \cos x}=$

$\frac{1}{\sin x \cos x}=$

$\frac{1}{\sin x}+\frac{1}{\cos x}=$

$\csc x \sec x$
How did you get from $\frac{1}{\sin x \cos x}=$ to
$\frac{1}{\sin x}+\frac{1}{\cos x}=$

5. Originally Posted by e^(i*pi)
How did you get from $\frac{1}{\sin x \cos x}=$ to
$\frac{1}{\sin x}+\frac{1}{\cos x}=$
Rookie mistake. Typo. Should've been a product, not a sum.

Fixed it. Thanks!