verify: (tan^(2)x+1)/(tanxcsc^(2)x)=tanx

⚑ Flag

Prove Identity: (tan²x + 1)/(tanxcsc²x) = tanx Use Pythagorean Identity to convert numerator: (sec²x)/(tanxcsc²x) = tanx Convert all functions to equivalent sin and cos expressions: (1/cos²x)/[(sinx/cosx)(1/sin²x)] = tanx Simplify denominator by cancelling out a sinx: (1/cos²x)/[(1/cosx)(1/sinx)] = tanx Convert denominator to single fraction: (1/cos²x)/(sinx/cosx) = tanx Convert left side from divison to multiplication operation by flip denominator fraction: (1/cos²x)(cosx/sinx) = tanx Simplify left side by cancelling out a cosx to conclude identity proof: sinx/cosx = tanxtanx = tanx