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Trigonometrische Identitäten Rechner

Mit unserem Trigonometrische Identitäten Schritt-für-Schritt-Rechner erhalten Sie detaillierte Lösungen für Ihre mathematischen Probleme. Üben Sie Ihre mathematischen Fähigkeiten und lernen Sie Schritt für Schritt mit unserem Mathe-Löser. Alle unsere Online-Rechner finden Sie hier.

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1

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

$\sec\left(x\right)^2+\csc\left(x\right)^2=\frac{1}{\sin\left(x\right)^2\cdot\cos\left(x\right)^2}$
2

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

$\sec\left(x\right)^2+\csc\left(x\right)^2$
3

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

$\frac{1}{\cos\left(x\right)^2}+\csc\left(x\right)^2$
4

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

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

The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

$L.C.M.=\cos\left(x\right)^2\sin\left(x\right)^2$
6

Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete

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

Rewrite the sum of fractions as a single fraction with the same denominator

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

Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$

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

Combine and simplify all terms in the same fraction with common denominator $\cos\left(x\right)^2\sin\left(x\right)^2$

$\frac{1}{\cos\left(x\right)^2\sin\left(x\right)^2}$
8

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

true

Endgültige Antwort auf das Problem

true

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