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- Express in terms of sine and cosine
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- Simplify into a single function
- Express in terms of Sine
- Express in terms of Cosine
- Express in terms of Tangent
- Express in terms of Cotangent
- Express in terms of Secant
- Express in terms of Cosecant
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Expand the fraction $\frac{1+\sin\left(x\right)^2}{\cos\left(x\right)^2}$ into $2$ simpler fractions with common denominator $\cos\left(x\right)^2$
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$\sec\left(x\right)^4+\tan\left(x\right)^4=\frac{1}{\cos\left(x\right)^2}+\frac{\sin\left(x\right)^2}{\cos\left(x\right)^2}$
Learn how to solve problems step by step online. Solve the trigonometric equation sec(x)^4+tan(x)^4=(1+sin(x)^2)/(cos(x)^2). Expand the fraction \frac{1+\sin\left(x\right)^2}{\cos\left(x\right)^2} into 2 simpler fractions with common denominator \cos\left(x\right)^2. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Since \cos is the reciprocal of \sec, \frac{1}{\cos\left(x\right)^2} is equivalent to \sec\left(x\right)^2. Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side.
