Question 1064867: Please help me find Cos(A-b) in the following equation.
Equation: https://s28.postimg.org/fbpu1fv25/tan_a_5.png
Thanks.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! cos (a-b)=cos a*cos b-sin a*sin b
A is a right triangle on the unit circle with adjacent -1, opposite -5, and hypotenuse sqrt (26).
B is a right triangle with adjacent -sqrt(5), opposite +2, and hypotenuse 3.
cos a=-1/sqrt (26)
cos b=-sqrt (5)/3. Their product is +sqrt (5)/3 sqrt (26), and rationalized that is sqrt (130)/78.
sin a =-5/sqrt(26)
sin b=2/3. Their product is -10/3 sqrt (26) and rationalized, that is -10 sqrt (26)/78. We are subtracting this second product from the first, so the answer is D, sqrt(130)+10 sqrt (26) divided all by 78.
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