Addition and subtraction formulas

12. [1.05/2 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 7.2.041. MY NOTES ASK YOUR TEACHER Prove the identity. tan(x) - tan(y) sin(x - y) 1 - tan(x) tan(y) cos(x + y) (tan(x) - tan(y))(cos(x) cos(y)) tan(x) - tan(y) 1 - tan(x) tan(y) (1 - tan(x) tan(y))( sin(x) . sin(y) X sin(x) cos(y) - cos(x) sin(y) = cos(x ) . cos (y ) - sin(x) sin(y) sin (x - y) cos(x + y)14. [0/1 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 7.2.048. MY NOTES ASK YOUR TEACHER Write the given expression in terms of x and y only. tan(sin-1(x) + cos-1(y)) X 15. [-/1 Points] DETAILS SPRECALC7 7.2.050. MY NOTES ASK YOUR TEACHER Write the given expression in terms of x and y only. sin(sin-1(x) + cos-1(y)) 16. [0/1 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 7.2.054.MI. MY NOTES ASK YOUR TEA calcPad + Operations Find the exact value of the expression. Functions sin(cos-1 () - tan-1 ()) X Symbols Relations Sets X VO O! Vectors Trig Submit AnswerSubmit Answer 17. [-/1 Points] DETAILS SPRECALC7 7.2.056. MY NOTES ASK YOUR TEACHER Evaluate the expression under the given conditions. sin(0 - 4); tan(0) = -, 0 in Quadrant III, sin() = -_ 3V 10 4 in Quadrant IV 1018. [3.15/7 Points] DETAILS PREVIOUS ANSWERS SPRECALC7 7.2.070. MY NOTES ASK YOUR TEACHER Refer to the figure. Show that a + 8 = y, and find the numerical value of tan(y). 5 B B Let ZA and LB be the two angles shown in the figure. Then, Y + A + B = 180 a + A = 90 B + B = 90 Subtracting the second and third equations from the first, we get 180 - 90 - 90 = (7 + A + B) - =Y. Find the numerical value of tan(y). tan(v) =