Final Answer
true
Step-by-step Solution
Specify the solving method
1
Starting from the left-hand side (LHS) of the identity
$\sin\left(x\right)\cos\left(x\right)\left(\tan\left(x\right)+\cot\left(x\right)\right)$
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$\sin\left(x\right)\cos\left(x\right)\left(\tan\left(x\right)+\cot\left(x\right)\right)$
Learn how to solve problems step by step online. Prove the trigonometric identity sin(x)cos(x)(tan(x)+cot(x))=1. Starting from the left-hand side (LHS) of the identity. Simplify \sin\left(x\right)\cos\left(x\right)\left(\tan\left(x\right)+\cot\left(x\right)\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x). Rewrite \tan\left(x\right)+\cot\left(x\right) in terms of sine an cosine. Multiplying fractions \frac{\sin\left(2x\right)}{2} \times \frac{1}{\sin\left(x\right)\cos\left(x\right)}.
Final Answer
true