Prove that cos9+sin9/cos9-sin9=tan54

Solution:- 

How to Prove 

• To prove cos9+sin9/cos9-sin9=tan54 we have to take tan54 R.H.S

• so, first step is replace tan(45+9) instead of tan54

• Now, put tan(A+B) formula that is tanA+tanB/1-tanA.tanB

• The equation becomes tan45+tan9/1-tan45.tan9, put the value of tan45 that is 1

• 1+tan9/1-tan9, Now consider tan9 as sin9/cos9

• On further solving we get cos9+sin9/cos9-sin9 which is R.H.S

• Hence L.H.S=R.H.S