Question

prove: (sinA+cosA)^2-1/tanA-sinA.cosA = 2cot^2a​

Answer 1

$\frac{( {sina + cosa})^{2} - 1}{tana - sinacosa} \\ = \frac{2sinacosa}{ \frac{sina - sia {cos}^{2} a}{cosa} } \\ = \frac{2sina {cos}^{2}a }{sina(1 - {cos}^{2}a )} \\ = 2\frac{ {cos}^{2}a }{ {sin}^{2} a} \\ = 2 {cot}^{2} a$