Step-by-step Solution

Prove the trigonometric identity $\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

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Step-by-step explanation

Problem to solve:

$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

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

$\frac{\sin\left(x\right)}{\cos\left(x\right)}+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)+cot(x)=sec(x)csc(x). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Apply the trigonometric identity: \cot\left(x\right)=\frac{\cos\left(x\right)}{\sin\left(x\right)}. Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. When multiplying two powers that have the same base (\sin\left(x\right)), you can add the exponents.

Final Answer

true
$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Related formulas:

1. See formulas

Time to solve it:

~ 0.06 s (SnapXam)