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?

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

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Answer 1 · 2018-07-27T11:14:41

#tan(t+x)=-63/16#

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#