Here, we show you a step-by-step solved example of trigonometry. This solution was automatically generated by our smart calculator:
Starting from the left-hand side (LHS) of the identity
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 $\frac{1}{2}$
Any expression multiplied by $1$ is equal to itself
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 $\frac{1}{2}$
Any expression multiplied by $1$ is equal to itself
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 $\frac{1}{2}$
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 $\frac{1}{2}$
Factor the difference of squares $\cos\left(t\right)^4-\sin\left(t\right)^4$ as the product of two conjugated binomials
Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$
Applying the pythagorean identity: $\cos^2(\theta)=1-\sin(\theta)^2$
Combining like terms $-\sin\left(t\right)^2$ and $-\sin\left(t\right)^{2}$
Since we have reached the expression of our goal, we have proven the identity
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