Question

prove tanA+ cotA = 2cosec2a
CotA- tanA = 2cot2A

Answer 1

 tan(A) + cot(A) = 2 cosec(2A) 

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 

(2)..
cos A . sin A 
-------- - -------- 
sin A . . cos A 

cos^2 A - sin^2 A 
-------------------------- 
. sin A . cos A 

cos 2A 
--------------- 
0.5sin 2A 

2cot 2A 

Answer 2

Answer:

Step-by-step explanation:

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