Find the general solution for 3tanx+cotx=5cosecx

Steps to solve Find the general solution for 3tanx+cotx=5cosecx

⇒3tanx+cotx=5cosecx

⇒3(sinx/cosx)+(cosx/sinx)=5/sinx

⇒3sin^2x+cos^2x=5cosx

⇒3(1-cos^2x)+cos^2x=5cosx

⇒3-5cosx-2cos^2x=0

⇒3-6cosx+cosx-2cos^2x=0

⇒3(1-2cosx)+cosx(1-2cosx)=0

⇒(1-2cosx)(3+cosx)=0

⇒1-2cosx=0 OR 3+cosx=0[Impossilbe]

⇒x=2nπ±π/3

Hence the general solution for 3tanx+cotx=5cosecx is 2nπ±π/3

Detain Information:-

Similar Questions For You:-

• Find the general solution for 4sin^2x+6cos^2x=5
• Find the general solution for tan^2x+sec^2x=3
• Find the general solution for secθ-1=(√2-1)tanθ
•  Find the general solution for 3tan^2θ-2sinθ=0