Question

Find the value of sin (a + b), cos (a + b), and tan (a + b), given
3
(i) sin a =3/5 and cosß =5/13
a and ß are in Quadrant I.

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Answer 1

Step-by-step explanation:

Since A is in Quadrant 2, cosA < 0. So, cosA = -√(1 - sin2A) = -√(1 - 9/25) = -4/5.

Since B is in Quadrant 1, cosB > 0. So, cosB = √(1 - sin2B) = √(1 - 25/169) = 12/13

cos(A+B) = (cosA)(cosB) - (sinA)(sinB) = (-4/5)(12/13) - (3/5)(5/13) = -63/65