Final Answer
Step-by-step Solution
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Starting from the right-hand side (RHS) of the identity
Rewrite $\frac{\cos\left(x\right)}{\sec\left(x\right)-\tan\left(x\right)}$ in terms of sine and cosine functions
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$\frac{\cos\left(x\right)}{\sec\left(x\right)-\tan\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1+sin(x)=cos(x)/(sec(x)-tan(x)). Starting from the right-hand side (RHS) of the identity. Rewrite \frac{\cos\left(x\right)}{\sec\left(x\right)-\tan\left(x\right)} in terms of sine and cosine functions. Divide fractions \frac{\cos\left(x\right)}{\frac{1-\sin\left(x\right)}{\cos\left(x\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Applying the pythagorean identity: \cos^2(\theta)=1-\sin(\theta)^2.