tan a=0,75 and cos b=0,6, a and b acute angles. calculate without calculator the value of cos(a-b)

Question

If tan a=0,75 and cos b=0,6 and both are acute angles calculate with out calculator cos(a-b)

Answer 1

0.75=¾, then tan(a)=3/4=sin(a)/cos(a). In the right triangle with leg lengths 3 and 4, the hypotenuse=√(3²+4²)=√25=5. Therefore, cos(b)=sin(a)=3/5=0.6 and sin(b)=cos(a)=4/5=0.8. This means that a+b=90°.

cos(a-b)≡cos(a)cos(b)+sin(a)sin(b)=cos(a)sin(a)+sin(a)cos(a)=2sin(a)cos(a)=2×0.6×0.8=0.96.