Question

what is the value of 1-cos2A/1+cos2A

Answer 1

Hi,
Since Cos(A+B)= CosA.CosB - SinA.SinB ( trigonometric identity)
=> Cos( A+A) = Cos2A = Cos²A - Sin²A
=> Cos²A -( 1-Cos²A)
=> 2Cos²A -1
=> 2(1-Sin²A)-1
=> 2 - 2Sin²A -1
=> 1–2Sin²A
=> 1- Sin²A -Sin²A
=> Cos²A - Sin²A
=> (Cos²A - Sin²A) / ( Cos²A + Sin²A) Since Cos²A + Sin²A = 1
Now, by dividing numerator & denominator by Cos²A
We get, Cos2A =( 1- tan²A) / (1+ tan²A) ………(1)●
NOW, by putting up the above value in
(1- Cos2A) / (1+Cos2A)
1 -Cos2A = 1 - ( 1-tan²A) /(1+tan²A)
= (1+tan²A - 1 + tan²A)
= 2tan²A / (1+tan²A)….(2)
Now similarly, 1+ Cos2A = 2/(1+ tan²A) …….(3)
Finally, (1-Cos2A) / (1+Cos2A)
= [2tan²A / (1+tan²A)] * [(1+tan²A) / 2 ]
= tan²A
Hope this helps U!!

Answer 2

Answer:

Tan square a thank u it might have helped u