Question

prove that tan A+cot A = 2 cosec 2A

Answer 1

Answer:

Step-by-step explanation:

LHS  

= tan(A) + cot(A)  

= sin(A)/cos(A) + cos(A)/sin(A)  

= [sin²(A) + cos²(A)]/[sin(A) cos(A)]  

= 1/[sin(A) cos(A)], since sin²(A) + cos²(A) = 1  

= 1/[(1/2) sin(2A)], from the identity sin(2A) = 2 sin(A) cos(A)  

= 2/sin(2A)  

= 2 cosec(2A)  

= RHS