Question

4Sintheta - Costheta / 4Sintheta +Costheta = 1/2 . then find cot theta​

Answer 1

Answer:

(4sintheta-costheta)/(4sintheta+costheta)=1/2

multiply by:

(4sintheta-costheta)/(4sintheta-costheta)in left side of the equation

then,

or,(4sintheta-costheta)^2/(4sintheta)^2-(costheta)^2=1/2

or, (16sin^2theta-8sintheta.costheta+cos^2theta)/(16sin^2theta-cos^2theta)=1/2

dividing by sin^2theta on denominator and numerator,then

or, (16-8cottheta+cot^2theta)/(16-cot^2theta)=1/2

or, 32-16cottheta+2 cot^2theta=16-cot^2theta

or,cot^2theta-16cottheta+16=0

or, cot^2theta-16cottheta+64-48=0

or, (cottheta-8)^2-48=0

or, (cottheta-8)^2=48

or, cottheta-8=√48

or, cottheta=√48 +8