Question

if tan A = 1 and tan B =√3 then find the value of cos A cosB- sinA× sin B

Answer 1

Hey,

TanA=1

=>TanA=Tan45=>A=45


TanB=√3

=>TanB=Tan60=>B=60.



Now,
cosAcosB-sinAsinB

=cos45cos60-sin45sin60

=1/√2×1/2-1/√2×√3/2

=1/2√2-√3/2√2

=(1-√3)/2√2.