Sin a=24/25,0<a<3.14/2; cos b=20/29, 0<b<3.14/2. Find tan (a+b)

Question

Find the exact value under the given conditions

Answer 1

Draw figures; use theorem of Pythagoras.

tan a = 24/7 and tan b = 21/20

Now use the addition formula for tan (a+b) to get the answer = -1.732051.

Note a + b is approximately 120° for which tan is -1.73.