Question

Sec²(0)/tan(0)=cot (0)+ tan(0) verify the identity

Answer 1

`\cfrac{\sec^2(\theta )}{\tan(\theta )}~~ = ~~\cot(\theta )+\tan(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sec^2(\theta )}{\tan(\theta )}\implies \cfrac{~~ ( 1^2 )/( \cos^2(\theta ) ) ~~}{(\sin(\theta ))/(\cos(\theta ))}\implies \cfrac{1}{\cos^2(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}\implies \cfrac{1}{\cos(\theta )\sin(\theta )}`

`\cfrac{\cos^2(\theta )+\sin^2(\theta )}{cos(\theta )\sin(\theta )}\implies \cfrac{\cos^2(\theta )}{cos(\theta )\sin(\theta )}+\cfrac{\sin^2(\theta )}{cos(\theta )\sin(\theta )} \\\\\\ \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\sin(\theta )}{cos(\theta )}\implies \cot(\theta )+\tan(\theta )`