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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:

$cos^4t-sin^4t=1-2sin^2t$
2

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

$\cos\left(t\right)^4-\sin\left(t\right)^4$

Simplify $\sqrt{\cos\left(t\right)^4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $\frac{1}{2}$

$\left(\cos\left(t\right)^{2}+\sqrt{1\sin\left(t\right)^4}\right)\left(\sqrt{\cos\left(t\right)^4}-\sqrt{1\sin\left(t\right)^4}\right)$

Any expression multiplied by $1$ is equal to itself

$\left(\cos\left(t\right)^{2}+\sqrt{\sin\left(t\right)^4}\right)\left(\sqrt{\cos\left(t\right)^4}-\sqrt{1\sin\left(t\right)^4}\right)$

Simplify $\sqrt{\sin\left(t\right)^4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $\frac{1}{2}$

$\left(\cos\left(t\right)^{2}+\sin\left(t\right)^{2}\right)\left(\sqrt{\cos\left(t\right)^4}-\sqrt{1\sin\left(t\right)^4}\right)$

Any expression multiplied by $1$ is equal to itself

$\left(\cos\left(t\right)^{2}+\sin\left(t\right)^{2}\right)\left(\sqrt{\cos\left(t\right)^4}-\sqrt{\sin\left(t\right)^4}\right)$

Simplify $\sqrt{\cos\left(t\right)^4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $\frac{1}{2}$

$\left(\cos\left(t\right)^{2}+\sin\left(t\right)^{2}\right)\left(\cos\left(t\right)^{2}-\sqrt{\sin\left(t\right)^4}\right)$

Simplify $\sqrt{\sin\left(t\right)^4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $4$ and $n$ equals $\frac{1}{2}$

$\left(\cos\left(t\right)^{2}+\sin\left(t\right)^{2}\right)\left(\cos\left(t\right)^{2}-\sin\left(t\right)^{2}\right)$
3

Factor the difference of squares $\cos\left(t\right)^4-\sin\left(t\right)^4$ as the product of two conjugated binomials

$\left(\cos\left(t\right)^{2}+\sin\left(t\right)^{2}\right)\left(\cos\left(t\right)^{2}-\sin\left(t\right)^{2}\right)$
4

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

$\cos\left(t\right)^{2}-\sin\left(t\right)^{2}$
5

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

$1-\sin\left(t\right)^2-\sin\left(t\right)^{2}$
6

Combining like terms $-\sin\left(t\right)^2$ and $-\sin\left(t\right)^{2}$

$1-2\sin\left(t\right)^{2}$
7

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

true

Risposta finale al problema

true

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