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Calcolatrice di Trigonometry

Risolvete i vostri problemi di matematica con la nostra calcolatrice Trigonometry passo-passo. Migliorate le vostre abilità matematiche con il nostro ampio elenco di problemi impegnativi. Trova tutte le nostre calcolatrici qui.

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1

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

$-cos\left(-x\right)+secx=tanxsinx$

Use the odd-even identity $\cos(-\theta)=\cos(\theta)$

$-\cos\left(x\right)+\sec\left(x\right)$
2

Start by simplifying the left side of the identity: $-\cos\left(-x\right)+\sec\left(x\right)$

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

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

$-\cos\left(x\right)+\sec\left(x\right)$
4

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

$-\cos\left(x\right)+\frac{1}{\cos\left(x\right)}$

Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator

$\frac{-\cos\left(x\right)\cos\left(x\right)+1}{\cos\left(x\right)}$

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

$\frac{-\cos\left(x\right)^2+1}{\cos\left(x\right)}$
5

Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator

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

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

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

Rewrite the exponent $\sin\left(x\right)^2$ as a product of $\sin\left(x\right)$

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

Separating the fraction's numerator

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

Apply the trigonometric identity: $\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$$=\tan\left(\theta \right)$

$\tan\left(x\right)\sin\left(x\right)$
7

Rewrite $\frac{\sin\left(x\right)^2}{\cos\left(x\right)}$ as $\tan\left(x\right)\sin\left(x\right)$ by applying trigonometric identities

$\tan\left(x\right)\sin\left(x\right)$
8

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

true

Risposta finale al problema

true

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