Find the exact value of cos​(alpha minus beta​) if sin alpha equals 0.5276 and cos beta equals 0.3488​, and both alpha and beta are​ first-quadrant angles?

1 Answer

#cos(alpha-beta)=0.7908#

Explanation:

#cos(alpha-beta)= cosalpha*cosbeta+sinalpha*sinbeta#

As #alpha# and #beta# are in #Q1#, all trigonometric ratios are positive. With #sinalpha=0.5276#, #cosalpha=sqrt(1-0.5276^2)=sqrt0.72163824=0.8495# and as #cosbeta=0.3488#, #sinbeta=sqrt(1-0.3488^2)=sqrt0.87833856=0.9372#

Substitute the given values:

#0.8495*0.3488+0.5276*0.9372#

= #0.2963056+0.49446672#

= #0.79077232~=0.7908#