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Starting from the left-hand side (LHS) of the identity
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$\frac{\cos\left(t\right)}{\sec\left(t\right)-\tan\left(t\right)}$
Learn how to solve problems step by step online. Prove the trigonometric identity cos(t)/(sec(t)-tan(t))=1+sin(t). Starting from the left-hand side (LHS) of the identity. Rewrite \frac{\cos\left(t\right)}{\sec\left(t\right)-\tan\left(t\right)} in terms of sine and cosine functions. Divide fractions \frac{\cos\left(t\right)}{\frac{1-\sin\left(t\right)}{\cos\left(t\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.