Hello,  find the exact value of each of the following under the given conditions.  sin alpha=3/5, 0<alpha<pi/2  ;   cos beta= (8sqrt113)/113, -pi/2<beta<0   (a) sin (alpha+beta)= -(4sqrt113)/565 (b) cos (alpha+beta)= (53sqrt113)/565 (c) sin (alpha-beta)= (52sqrt113)/565 (d) tan (alpha-beta)= ?  I got the answers for (a to c), the correct answers, but I couldn't get (d) correct. I got the answer 53/4 instead of 52/11, which is the correct answer for (d). I used the sum and difference formulas for each of them, yet I don't understand how 52/11 is the correct answer. Can you explain how it is 52/11?

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.