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Prove the trigonometric identity $\frac{\tan\left(x\right)+\cos\left(x\right)}{\sin\left(x\right)}=\sec\left(x\right)+\cot\left(x\right)$

Step-by-step Solution

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Final Answer

true

Step-by-step Solution

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Starting from the left-hand side (LHS) of the identity

$\frac{\tan\left(x\right)+\cos\left(x\right)}{\sin\left(x\right)}$

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$\frac{\tan\left(x\right)+\cos\left(x\right)}{\sin\left(x\right)}$

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Learn how to solve problems step by step online. Prove the trigonometric identity (tan(x)+cos(x))/sin(x)=sec(x)+cot(x). Starting from the left-hand side (LHS) of the identity. Expand the fraction \frac{\tan\left(x\right)+\cos\left(x\right)}{\sin\left(x\right)} into 2 simpler fractions with common denominator \sin\left(x\right). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Divide fractions \frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\sin\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.

Final Answer

true

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Prove from RHS (right-hand side)Express everything into Sine and Cosine

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Function Plot

Plotting: $true$

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