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Question
\frac{\cos\left(a\right)}{1}-\tan\left(a\right)\times \frac{\sin\left(a\right)}{1}-\cot\left(a\right)
Simplify the expression
2\cos\left(a\right)-\sec\left(a\right)-\cot\left(a\right)
Evaluate
\frac{\cos\left(a\right)}{1}-\tan\left(a\right)\times \frac{\sin\left(a\right)}{1}-\cot\left(a\right)
Divide the terms
\frac{\cos\left(a\right)}{1}-\tan\left(a\right)\sin\left(a\right)-\cot\left(a\right)
Divide the terms
\cos\left(a\right)-\tan\left(a\right)\sin\left(a\right)-\cot\left(a\right)
Transform the expression
More Steps
Evaluate
-\tan\left(a\right)\sin\left(a\right)
\text{Use }\tan t = \frac{\sin t}{\cos t}\text{ to transform the expression}
-\frac{\sin\left(a\right)}{\cos\left(a\right)}\times \sin\left(a\right)
Multiply the terms
-\frac{\sin\left(a\right)\sin\left(a\right)}{\cos\left(a\right)}
Multiply the terms
-\frac{\sin^{2}\left(a\right)}{\cos\left(a\right)}
\cos\left(a\right)-\frac{\sin^{2}\left(a\right)}{\cos\left(a\right)}-\cot\left(a\right)
Subtract the terms
More Steps
Evaluate
\cos\left(a\right)-\frac{\sin^{2}\left(a\right)}{\cos\left(a\right)}
Reduce fractions to a common denominator
\frac{\cos\left(a\right)\cos\left(a\right)}{\cos\left(a\right)}-\frac{\sin^{2}\left(a\right)}{\cos\left(a\right)}
Write all numerators above the common denominator
\frac{\cos\left(a\right)\cos\left(a\right)-\sin^{2}\left(a\right)}{\cos\left(a\right)}
Multiply the terms
\frac{\cos^{2}\left(a\right)-\sin^{2}\left(a\right)}{\cos\left(a\right)}
\frac{\cos^{2}\left(a\right)-\sin^{2}\left(a\right)}{\cos\left(a\right)}-\cot\left(a\right)
Reduce fractions to a common denominator
\frac{\cos^{2}\left(a\right)-\sin^{2}\left(a\right)}{\cos\left(a\right)}-\frac{\cot\left(a\right)\cos\left(a\right)}{\cos\left(a\right)}
Write all numerators above the common denominator
\frac{\cos^{2}\left(a\right)-\sin^{2}\left(a\right)-\cot\left(a\right)\cos\left(a\right)}{\cos\left(a\right)}
Transform the expression
More Steps
Evaluate
\cos^{2}\left(a\right)-\sin^{2}\left(a\right)-\cot\left(a\right)\cos\left(a\right)
\text{Use }\sin^2 t = 1 - \cos^2 t\text{ to transform the expression}
\cos^{2}\left(a\right)-\left(1-\cos^{2}\left(a\right)\right)-\cot\left(a\right)\cos\left(a\right)
Calculate
\cos^{2}\left(a\right)-1+\cos^{2}\left(a\right)-\cot\left(a\right)\cos\left(a\right)
Add the terms
More Steps
Evaluate
\cos^{2}\left(a\right)+\cos^{2}\left(a\right)
Collect like terms by calculating the sum or difference of their coefficients
\left(1+1\right)\cos^{2}\left(a\right)
Add the numbers
2\cos^{2}\left(a\right)
2\cos^{2}\left(a\right)-1-\cot\left(a\right)\cos\left(a\right)
\frac{2\cos^{2}\left(a\right)-1-\cot\left(a\right)\cos\left(a\right)}{\cos\left(a\right)}
Transform the expression
2\cos\left(a\right)-\frac{1}{\cos\left(a\right)}-\cot\left(a\right)
Solution
2\cos\left(a\right)-\sec\left(a\right)-\cot\left(a\right)
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