If tanA=1/5, tanB=2/3 show that cos2A=cos2B

Steps to solve 
If tanA=1/5, tanB=2/3 show that cos2A=cos2B

We know that

[cos2A=1-tan^2A/1+tan^2A]

[sin2A=2tanA/1+tan^2A]

cos2A=1-tan^2A/1+tan^2A=(1-1/25)/(1+1/25)=12/13

sin2B=2tanB/1+tan^2B=2(2/3)/(1+4/9)=(4/3)/(13/9)=12/13

Hence  cos2A=cos2B Proved.

Detail Information:-

Similar questions for you:-

• If A+C=B, Show that the tanA.tanB.tanC=tanB-tanA-tanC
• If tanθ=(asinx+bsiny)/(acosx+bcosy) then show that asin(θ–x)+bsin(θ-y)=0
•  If secA-tanA=1/2 and 0 less than A less than 90 then show that secA=5/4
• If tanθ=b/a than the value of acos2θ+bsin2θ