Question 633150
find the exact value given the following conditions 
a. cos (a + b)
b. sin (a + b)
c. tan (a + b) 
sin a = 5/6, pi/2 < a < pi, and tan b = 3/7, pi < b < 3pi/2
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O=opposite side
A=adjacent side
H=hypotenuse
..
a is a reference angle in quadrant II where sin>0 and cos<0
sin a=5/6=O/H (given)
A=&#8730;(H^2-O^2)=&#8730;(36-25)=&#8730;11
cos a=-&#8730;11/6
tan a=-5/&#8730;11
.. 
b is a reference angle in quadrant III where both sin and cos<0
tan b=3/7=O/A (given)
H=&#8730;(O^2+A^2)=&#8730;(9+49)=&#8730;58
sin b=–3/&#8730;58
cos b=–7/&#8730;58
..
a. cos (a + b)
=cos a*cos b-sin a*sin b
=[-&#8730;11/6*-7/&#8730;58]-[(5/6)*(-3&#8730;58)]=(7&#8730;11+15)/(6&#8730;58)
..
b. sin (a + b)
=sin a*cos b+cos a*sin b
=[(5/6)*(-7/&#8730;58)+[(-&#8730;11/6)*(-3/&#8730;58)]
=(-35+3&#8730;11)/(6&#8730;58)
..
tan(a + b)
=(tan a+tan b)/(1-tan a tan b)
=[(-5/&#8730;11)+(3/7)]/[1-(-5/&#8730;11)(3/7)]