cotxsinx - cosx + cosx
Does this equal cos x ?
cos/sin * sin = cosx
cot(x) = cos(x)/sin(x)
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Now you have:
[cos(x)/sin(x)] - cos(x) + cos(x)
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What's the answer?
By the way, the person who just commented is me. I should've changed my name.
cotxsinx - cosx + cosx
Putting in cotx = (cos/sinx),
(cosx/sinx)*sinx + (- cosx + cosx)
= cosx*(sinx/sinx) + 0
= cosx*1
= cosx
To determine if cot(x)sin(x) - cos(x) + cos(x) equals cos(x), we can simplify the expression step by step.
1. Start with the given expression: cot(x)sin(x) - cos(x) + cos(x).
2. Recall that cot(x) is equal to cos(x)/sin(x). So substitute cot(x) with cos(x)/sin(x).
The expression becomes: (cos(x)/sin(x))sin(x) - cos(x) + cos(x).
3. Simplify each term separately:
- (cos(x)/sin(x))sin(x) simplifies to just cos(x), as the sin(x) terms cancel out.
The expression now becomes: cos(x) - cos(x) + cos(x).
4. Combine like terms: cos(x) - cos(x) + cos(x) simplifies to just cos(x).
5. Therefore, the simplified expression is equal to cos(x).
So, yes, cot(x)sin(x) - cos(x) + cos(x) does equal cos(x).