How do you simplify the expression #sin (arctan (1/4) + arccos (3/4) )#?

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Answer 1 · 2016-06-26T14:25:47

#sin (arctan(1/4)+arccos(3/4))=(3sqrt17+4sqrt119)/68#

Let #A=arctan(1/4)#
Let #B=arccos(3/4)#

#sin (A+B)=sin A cos B + cos A sin B#

#sin (A+B)=(1/sqrt17)(3/4) + (4/sqrt17) (sqrt7/4)#

#sin (A+B)=(3+4sqrt7)/(4sqrt17)#

#sin (A+B)=(3sqrt17+4sqrt119)/68#

#sin (arctan(1/4)+arccos(3/4))=(3sqrt17+4sqrt119)/68#

God bless....I hope the explanation is useful.