Question

if tan alpha=1 and tan beta=√3 evaluate cos alpha cos beta - sin alpha sin bheta​

Answer 1

Answer:

tan alpha=1=tan 45°

alpha= 45°

tan beta =√3=tan 60°

beta= 60°

cos alpha cos beta -sin alpha sin beta

cos 45° cos 60° - sin 45° sin 60°

(1/√2)(1/2) - (1/√2)(√3/2)

1/2√2 - √3/2√2

(1-√3)/2√2

(1-√3)×√2/2√2×√2

(√2-√6)/4