Question 1040635
If cosA = 8/17 and cosecB = 5/4 and both A and B are acute angles. Calculate the value of cos(A-B) without using a calculator.
<pre>{{{cos (A) = 8/17 = A/H}}};                                              {{{matrix(1,3, csc (B) = 5/4, or, sin (B) = 4/5 = O/H = y/r)}}}
{{{sin (A) = O/H = y/r = 15/17}}} ----- 8-15-17 special right triangle       {{{cos (B) = A/H = x/r = 3/5}}} ------ 3-4-5 special right triangle

cos (A - B) = cos A cos B + sin A sin B
cos (A - B) = {{{(8/17) * (3/5) + (15/17) * (4/5)}}} 
cos (A - B) = {{{24/85 + 60/85}}} ------- No cancellation was done since it's easier to obtain final answer with the current denominators
{{{highlight_green(cos (A - B) = 84/85)}}}