Step-by-step Solution

Prove the trigonometric identity $\csc\left(x\right)-\sin\left(x\right)=\cot\left(x\right)\cos\left(x\right)$

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Step-by-step Solution

Problem to solve:

$\csc x-\sin x=\cot x\cos x$

Solving method

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

$\frac{1}{\sin\left(x\right)}-\sin\left(x\right)=\cot\left(x\right)\cos\left(x\right)$

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)-sin(x)=cot(x)cos(x). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Combine all terms into a single fraction with \sin\left(x\right) as common denominator. When multiplying two powers that have the same base (\sin\left(x\right)), you can add the exponents. Apply the trigonometric identity: 1-\sin\left(x\right)^2=\cos\left(x\right)^2.

Final Answer

true
$\csc x-\sin x=\cot x\cos x$

Related Formulas:

2. See formulas

Time to solve it:

~ 0.61 s