Question 1159220
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Use the formula for sum of arguments


    cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b)    (1)


You need to know sin(a) and sin(b) and cos(b)


sin(a) = +/- {{{sqrt(1-cos^2(a))}}} = +/- {{{sqrt(1-(24/25)^2)}}} = +/- {{{sqrt(49/625)}}} = +/- {{{7/25}}},

and since  sin(a) < 0, according to the condition, we chose  sin(a) = -{{{7/25}}}.    (2)



Next, b = {{{11pi/6}}} = {{{2pi-pi/6}}};

therefore, sin(b) = -{{{1/2}}};  cos(b) = {{{sqrt(3)/2}}}.    (3)


Now the last YOUR step is to substitute  (2) and (3) into the formula (1).


You do it and complete the calculations on your own.
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