Question

Cot - tan = 2cos-1/sin cos

Answer 1

Answer:

Step-by-step explanation:

Given:

To prove that:

          cot A - tan A =  \frac{2cosA^2-1}{sinAcosA}

Proof:

We know that,

tan A =  \frac{sin A}{cos A} ,

cot A =  \frac{cos A}{sin A}  

LHS = cot A - tan A

=>  \frac{cos A}{sin A} -  \frac{sin A}{cos A}  

=>  \frac{cos^2A - sin^2A}{sinAcosA}  

We know that,

=> sin^2 A + cos^2A =1  

=> sin^2 A = 1 - cos^2A

=> - sin^2A = cos^2A - 1

Hence,

=>  \frac{cos^2A +(- sin^2A)}{sinAcosA}  

=>  \frac{cos^2A+ (cos^2A-1) }{sinA cosA}  

=>  \frac{2cos^2A - 1}{sinAcosA}  

=> RHS,

                ∴ Hence proved

Answer 2

Answer:

Step-by-step explanation:

Refer to attachment