Can someone tell me the solution of following problems:
1.
$(sin(pi/2 - x) - cos^3x)/(sin(2x + 4pi))$

My solution sinx/2

2.
I have to get other 2 values
sinx=2/3
_______
sin2x = ?
tan(pi/4-x) = ?

3.
y = x/5 - 1
y = -5x/4 + 1

k1 = 1/5
k2 = -5/4

$tan()=|(k2-k1)/(1+k1*k2)|$

2. 1.) Yes, assuming that you are supposed to simplify that expression, I'm also arriving at $\frac{sinx}{2}$.

2.) Hmm, I think there's some information missing here. In order to evaluate $sin2x$, you could use the identity $sin2x=2sinxcosx$. Since you have the value of $sinx$, $cosx$ can be found using $sin^2x + cos^2x = 1$ - but that gives two values for $cosx$, one positive and another negative. Usually, these type of questions will give a rage for the value of x, or make a comment such as "x is an acute angle", so that you can determine whether $cosx$ is positive or negative.

3.) Please be clearer. Specifically, $tan()$ makes literally no sense.

3. 2.) Lets say it is positive. For cosx I get square root of 5 divided by 3. For tanx I get 2 times square root of 5 divided by 5.

Now I put this values to get sin2x (my solution is 4 times square root of 5 divided by 9) and to get tan(pi/4 - x), my solution to this is 1 - (2 times square root of 5 divided by 5) / 1 + (2 times square root of 5 divided by 5)

3.) I ment tanφ

and my solution is: 62° 39'

Thank you very much.