What is the exact value of tan(t+x) given that sin(t)=3/5 and sin(x)=12/13 knowing that t & x are between 0 and pi/2 and that the sides are Pythagorean triples?

Homework question stumping.. I came up with 56/33 trying to confirm and validate. Thanks!

1 Answer
Jul 27, 2018

tan(t+x)=-63/16

Explanation:

If angle t is 0 < t < pi/2, then t is in the first quadrant. Using a right-angled triangle,

sint=3/5

cost=4/5 (cos is positive in the first quadrant)

tant=3/4 (tan is positive in the first quadrant)

If angle x is also 0 < x < pi/2, then x is in the first quadrant. Using a right-angled triangle,

sinx=12/13

cosx=5/13 (cos is positive in the first quadrant)

tanx=12/5 (tan is positive in the first quadrant)

tan(t+x)

=(tant+tanx)/(1-tant tanx)

=(3/4+12/5)/(1-3/4times12/5)

=(63/20)/(1-9/5)

=63/20times-5/4

=-63/16