Here, we show you a step-by-step solved example of express in terms of sine and cosine. This solution was automatically generated by our smart calculator:
Rewrite $1-\tan\left(x\right)$ in terms of sine and cosine functions
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator
In the original expression, replace the $1-\tan\left(x\right)$ with $\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}$
Rewrite $1+\tan\left(x\right)$ in terms of sine and cosine functions
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator
In the original expression, replace the $1+\tan\left(x\right)$ with $\frac{\cos\left(x\right)+\sin\left(x\right)}{\cos\left(x\right)}$
We can simplify the quotient of fractions $\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{\frac{\cos\left(x\right)+\sin\left(x\right)}{\cos\left(x\right)}}$ by inverting the second fraction and multiply both fractions
Simplify the fraction
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