Question

Prove :-
sec 8A-1/ sec 4A-1 = tan 8A/ tan 2A
can this sum be solved using cos 2A formula ​

Answer 1

Answer:

Step-by-step explanation:

Given, (sec8A - 1) / (sec4A - 1) 

=> (1/cos8A) - 1) / (1/cos4A) - 1

=> (1 - cos8A)/cos8A) / (1 - cos4A) / cos4A) 

=> cos4A (1 - cos8a) / (cos8A (1 - cos4A)) 

=> cos4A(1 - (1 - 2sin²4A)) / cos8A (1 - (1 - 2sin²2A))

=> 2cos4A sin²4A / (2cos8A sin²2A) 

=> (2 cos4A sin4A) sin4A / (2 cos8A sin²2A) 

=> sin8A sin4A / (2 cos8A sin²2A) 

=> tan 8A * (sin 4A / 2 sin²2A)

=> tan8A * (2sin2Acos2A/2sin²2A)

=> tan 8A * (cos 2A / sin 2A)

=> tan8A* 1/(sin2A/cos2A)

=> tan 8A/tan 2A