Final Answer
Step-by-step Solution
Specify the solving method
Starting from the right-hand side (RHS) of the identity
Factor the polynomial $\sin\left(x\right)+\sin\left(x\right)^2$ by it's greatest common factor (GCF): $\sin\left(x\right)$
Learn how to solve trigonometric identities problems step by step online.
$\frac{\sin\left(x\right)+\sin\left(x\right)^2}{\cos\left(x\right)\left(1+\sin\left(x\right)\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)=(sin(x)+sin(x)^2)/(cos(x)(1+sin(x))). Starting from the right-hand side (RHS) of the identity. Factor the polynomial \sin\left(x\right)+\sin\left(x\right)^2 by it's greatest common factor (GCF): \sin\left(x\right). Simplify the fraction \frac{\sin\left(x\right)\left(1+\sin\left(x\right)\right)}{\cos\left(x\right)\left(1+\sin\left(x\right)\right)} by 1+\sin\left(x\right). Apply the trigonometric identity: \frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}=\tan\left(\theta \right).