Question

if a cosx- b sinx = c ' show that a sinx+b cosx = +-√a^2+b^2-c^2.​

Answer 1

Step-by-step explanation:

a cos x+b sin x= c , divide both sides by(a^2+b^2)^1/2.

a/(a^2+b^2)^1/2.cos x+b/(a^2+b^2)^1/2.sin x=c/(a^2+b^2)^1/2.

Let a/(a^2+b^2)^1/2=sin A , then b/(a^2+b^2)^1/2=cosA

sinA.cos x+cos A.sin x=c/(a^2+b^2)^1/2

sin (A+x)= c/(a^2+b^2)^1/2

A+x=sin inverse c/(a^2+b^2)^1/2

x=sin inverse c/(a^2+b^2)^1/2-A

x=sin inverse c/(a^2+b^2)^1/2 - sin inverse a/(a^2+b^2)^1/2. , answer.

Hope it helps..

Answer 2

Step-by-step explanation:

cosx- bsinx=c

sinx +b cosx-=0+-√a²+b² -c²

sinx + b cosx-=0-c

cosx+ b sinx =c