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# Trigonometry Calculator

## Get detailed solutions to your math problems with our Trigonometry step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of trigonometry. This solution was automatically generated by our smart calculator:

$\sec\left(x\right)-\sin\left(x\right)\tan\left(x\right)=\cos\left(x\right)$
2

Starting from the left-hand side (LHS) of the identity

$\sec\left(x\right)-\sin\left(x\right)\tan\left(x\right)$
3

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\sec\left(x\right)+\sin\left(x\right)\frac{-\sin\left(x\right)}{\cos\left(x\right)}$

Multiplying the fraction by $\sin\left(x\right)$

$\sec\left(x\right)+\frac{-\sin\left(x\right)\sin\left(x\right)}{\cos\left(x\right)}$

When multiplying two powers that have the same base ($\sin\left(x\right)$), you can add the exponents

$\sec\left(x\right)+\frac{-\sin\left(x\right)^2}{\cos\left(x\right)}$
4

Multiplying the fraction by $\sin\left(x\right)$

$\sec\left(x\right)+\frac{-\sin\left(x\right)^2}{\cos\left(x\right)}$
5

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\frac{1}{\cos\left(x\right)}+\frac{-\sin\left(x\right)^2}{\cos\left(x\right)}$
6

Combine fractions with common denominator $\cos\left(x\right)$

$\frac{1-\sin\left(x\right)^2}{\cos\left(x\right)}$
7

Apply the trigonometric identity: $1-\sin\left(\theta \right)^2$$=\cos\left(\theta \right)^2$

$\frac{\cos\left(x\right)^2}{\cos\left(x\right)}$
8

Simplify the fraction $\frac{\cos\left(x\right)^2}{\cos\left(x\right)}$ by $\cos\left(x\right)$

$\cos\left(x\right)$
9

Since we have reached the expression of our goal, we have proven the identity

true

##  Final answer to the problem

true

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