Question 719857
Find the exact value of each of the following under the given conditions:
{{{cotA= -24/7}}} {{{pi/2 < A < pi}}} {{{cosB= 5/6}}} {{{0 < B < pi/2 }}}

{{{sin (A+B)}}}
{{{cos (A-B)}}}
{{{sin (A-B)}}}
{{{tan (A+B) }}}
***
let o=opposite side
let a=adjacent side
let h=hypotenuse
..
&#960;/2 < A < &#960; (quadrant II)
cotA=-24/7=a/o
a=-24, o=7
h=&#8730;(o^2+24^2)=&#8730;(49+576)=&#8730;625=25
sinA=o/h=7/25
cosA=a/h=-24/25
tanA=o/a=-7/24
...
0 < B < &#960;/2 (quadrant I)
cosB=5/6=a/h
a=5, h=6
o=&#8730;(h^2-a^2)=&#8730;(36-25)=&#8730;11
sinB=o/h=&#8730;11/6
cosB=a/h=5/6
tanB=o/a=&#8730;11/5
...
Identity: sin(A+B)=sinAcosB+cosAsinB
=7/25*5/6+(-24/25*&#8730;11/6)
=35/150-24&#8730;11/150=(35-24&#8730;11)/150
...
Identity: sin(A-B)=sinAcosB-cosAsinB
=7/25*5/6-(-24/25*&#8730;11/6)
=35/150+24&#8730;11/150
=(35+24&#8730;11)/150
...
Identity:cos(A-B)=cosAcosB+sinAsinB
=-24/25*5/6+7/25*&#8730;11/6
=-120/150+7&#8730;11/150
=-120+7&#8730;11/150
...
Identity:tan(A+B)=(tanA+tanB)/(1-tanAtanB)
=(-7/24+&#8730;11/5)/(1-(-7/24*&#8730;11/5)
=(-7/24+&#8730;11/5)/(1+7&#8730;11/120)