2 cos ( x – pie/2) + 3 sin (x + pie/2) - (3sin x + 2cos x )
first, that's pi, not pie!
Don't any teachers actually show how to spell Greek letters any more?
2 cos(x - π/2) + 3 sin(x + π/2) - (3sinx + 2cosx)
= 2sinx + 3cosx - 3sinx - 2cosx
= cosx - sinx
You must be studying the sum/difference formulas for sin and cos.
Better review them some more.
use the sin(A+B) and cos(A-B) expansions
2 cos ( x – π/2) + 3 sin (x + π/2) - (3sin x + 2cos x )
= 2(cosx*coxπ/2) + sinx*sinπ/2) + 3(sinx*cosπ/2 + cosx*sinπ/2) - 3sinx - 2cosx
= 2(cosx*0 + sinx*1) + 3(sinx*0 + cosx*1) - 3sinx - 2cosx
= ....
carry on
Thank u so much sir.
To simplify the given expression, we can start by expanding and simplifying each term separately. Let's go step by step:
1. Expand the first term:
2 cos (x - π/2) = 2(cos x cos(π/2) + sin x sin(π/2))
= 2(cos x * 0 + sin x * 1)
= 2 sin x
2. Expand the second term:
3 sin (x + π/2) = 3(sin x * cos(π/2) + cos x * sin(π/2))
= 3(sin x * 0 + cos x * 1)
= 3 cos x
3. Expand the third term:
-(3sin x + 2cos x) = -3 sin x - 2 cos x
Now we can substitute the expanded expressions back into the original equation:
2 sin x + 3 cos x - (3 sin x + 2 cos x)
Now we can simplify further:
2 sin x + 3 cos x - 3 sin x - 2 cos x
Combine like terms:
(-1 sin x) + (1 cos x)
Finally, we can rewrite this as:
cos x - sin x
Hence, the simplified form of the given expression is cos x - sin x.