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# Prove the trigonometric identity $1+\sec\left(x\right)^2\sin\left(x\right)^2=\sec\left(x\right)^2$

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true

##  Step-by-step Solution 

How should I solve this problem?

• Prove from LHS (left-hand side)
• Prove from RHS (right-hand side)
• Express everything into Sine and Cosine
• Exact Differential Equation
• Linear Differential Equation
• Separable Differential Equation
• Homogeneous Differential Equation
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
Can't find a method? Tell us so we can add it.
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Starting from the left-hand side (LHS) of the identity

$1+\sec\left(x\right)^2\sin\left(x\right)^2$
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Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

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

Learn how to solve trigonometric identities problems step by step online.

$1+\sec\left(x\right)^2\sin\left(x\right)^2$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1+sec(x)^2sin(x)^2=sec(x)^2. Starting from the left-hand side (LHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Multiplying the fraction by \sin\left(x\right)^2. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}.

true

##  Explore different ways to solve this problem

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###  Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.

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