cosecA+cotA=cot A/2

Question

solution of answer.

Answer 1

Remeber the formula Sin2A = 2SinACosA

SinA = 2Sin(A/2)Cos(A/2)

Cos2A = 2Cos^2(A)-1

CosA = 2Cos^2(A/2)-1

Left handside identity = CosecA+CotA

= 1/SinA + CosA/SinA

= (1+CosA)/SinA

= (1+2Cos^2A/2-1)/(2SinA/2CosA/2)

= (2Cos^2A)/2/(2SinA/2CosA/2)

= (CosA/2)/(SinA/2)

= CotA/2

= Right hand side identity