Question

Please help me ,
have I simplified it correctly

Answer 1

@ganeshie8 @mathmate

Answer 2

\[\huge \frac{ \tan(x-\frac{ \pi }{ 2 })\cos(\frac{ 3\pi }{ 2 }+x)-\sin ^{3}(\frac{ 7\pi }{ 2 }-x) }{ \cos(x-\frac{ \pi }{ 2 })\tan(\frac{ 3\pi }{ 2 }+x) }\]

Answer 3

\[\frac{ \tan(x-\frac{ \pi }{ 2 })\cos(\frac{ 3\pi }{ 2 }+x)-\sin ^{3}(\frac{ 7\pi }{ 2 }-x) }{ \cos(x-\frac{ \pi }{ 2 })\tan(\frac{ 3\pi }{ 2 }+x) }\]

Answer 4

One way to check simplification is to put in numbers and check.
If they are not equal, there is definitely an error. If they are equal for different values of x, then there is a good chance that it is correct.

Answer 5

Unfortunately they don't match, so a thorough checking is required.

Answer 6

for cos, noticing \(\large x + \frac{3\pi}{2} \equiv x - \frac{\pi}{2} \) may help in simplifying the expression a bit smoothly..

Answer 7

they are different right?

Answer 8

they are equal for cosine, as adding/subtracting 2pi to the angle wont change the value of a cosine function