Step-by-step Solution

Prove the trigonometric identity $\sec\left(x\right)-\sec\left(x\right)\sin\left(x\right)^2=\cos\left(x\right)$

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Step-by-step Solution

Problem to solve:

$\sec\left(x\right)-\sec\left(x\right)\sin^2\left(x\right)=\cos\left(x\right)$

Solving method

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

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

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sec(x)-sec(x)*sin(x)^2=cos(x). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Add fraction's numerators with common denominators: \frac{1}{\cos\left(x\right)} and \frac{-\sin\left(x\right)^2}{\cos\left(x\right)}. Apply the trigonometric identity: 1-\sin\left(x\right)^2=\cos\left(x\right)^2.

Final Answer

true
$\sec\left(x\right)-\sec\left(x\right)\sin^2\left(x\right)=\cos\left(x\right)$

Related Formulas:

2. See formulas

Time to solve it:

~ 0.49 s