Prove the identity. (cot^(2)x)/(csc x+1)=csc x-1 Note that each Statement must be based on a Rule chosen from the Rule menu. To se the right of the Rule. Statement

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Prove the identity.  (cot^(2)x)/(csc x+1)=csc x-1 Note that each Statement must be based on a Rule chosen from the Rule menu. To se the right of the Rule. Statement

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Start with left-hand side: We start with the left-hand side of the identity and try to transform it into the right-hand side. We have: (cot^(2)x)/(csc x+1) Recall the trigonometric identities: cot(x) = 1/tan(x) and csc(x) = 1/sin(x)Rewrite cot(x): Rewrite cot(x) in terms of sin(x) and cos(x): cot(x) = cos(x)/sin(x) So, cot^(2)x = (cos(x)/sin(x))^2Rewrite left-hand side: Now, let's rewrite the left-hand side using the cot(x) in terms of sin(x) and cos(x): (cot^(2)x)/(csc x+1) = ((cos(x)/sin(x))^2) / (1/sin(x) + 1)Multiply by sin(x): Multiply both numerator and denominator by sin(x) to get rid of the fraction in the denominator: ((cos(x)/sin(x))^2) * sin(x) / ((1/sin(x) + 1) * sin(x)) = (cos^2(x)/sin^2(x)) * sin(x) / (1 + sin(x))Simplify expression: Simplify the expression by canceling out a sin(x) in the numerator and denominator: (cos^2(x)/sin(x)) / (1 + sin(x)) = cos^2(x) / (sin(x) * (1 + sin(x)))Use Pythagorean identity: Use the Pythagorean identity: sin^2(x) + cos^2(x) = 1 So, cos^2(x) = 1 - sin^2(x) Replace cos^2(x) in the expression: (1 - sin^2(x)) / (sin(x) * (1 + sin(x)))Factor numerator: Factor the numerator as a difference of squares: ((1 - sin(x)) * (1 + sin(x))) / (sin(x) * (1 + sin(x)))Cancel common factor: Cancel out the common factor (1 + sin(x)) in the numerator and denominator: (1 - sin(x)) / sin(x)Rewrite 1/sin(x): Rewrite 1/sin(x) as csc(x): csc(x) - sin(x)/sin(x) = csc(x) - 1Transform into right-hand side: We have now transformed the left-hand side of the identity into the right-hand side: (cot^(2)x)/(csc x+1) = csc x - 1 This completes the proof.

Prove the identity. $\newline$ $\frac{\cot ^{2} x}{\csc x+1}=\csc x-1$ $\newline$ Note that each Statement must be based on a Rule chosen from the Rule menu. To se the right of the Rule. $\newline$ Statement

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Prove the identity.\newlinecot⁡2xcsc⁡x+1=csc⁡x−1 \frac{\cot ^{2} x}{\csc x+1}=\csc x-1 cscx+1cot2x​=cscx−1\newlineNote that each Statement must be based on a Rule chosen from the Rule menu. To se the right of the Rule.\newlineStatement

Prove the identity. $\newline$ $\frac{\cot ^{2} x}{\csc x+1}=\csc x-1$ $\newline$ Note that each Statement must be based on a Rule chosen from the Rule menu. To se the right of the Rule. $\newline$ Statement