If #acostheta+bsintheta=c#, what is the value of #asintheta-bcostheta#?

1 Answer
Dec 5, 2017

Please see below.

Explanation:

Squaring each side of #acostheta+bsintheta=c#

#a^2cos^2theta+b^2sin^2theta+2ab sinthetacostheta=c^2#

or #a^2(1-sin^2theta)+b^2(1-cos^2theta)+2ab sinthetacostheta=c^2#

or #a^2sin^2theta+b^2cos^2theta-2ab sinthetacostheta=a^2+b^2-c^2#

or #(asintheta-bcostheta)^2=a^2+b^2-c^2#

i.e. #asintheta-bcostheta=+-sqrt(a^2+b^2-c^2)#