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Question

Can anyone help me to solve this sum

Use the compound angle formulae to find the following in surd form:
1) tan 75
2) tan 285

Answer 1

1) tan 75 = tan (120 - 45)
= (tan 120 - tan 45)/(1 + tan 120 tan 45)
= (-sqrt(3) - 1)/(1 - sqrt(3))
= -(sqrt(3) + 1)^2/(1 - 3)
= (1/2)(3 + 2sqrt(3) + 1)
= 2 + sqrt(3)

2) tan 285 = tan (240 + 45)
= (tan 240 + tan 45)/(1 - tan 240 tan 45)
= (sqrt(3) + 1)/(1 - sqrt(3))
= -(1/2)(sqrt(3) + 1)^2
= -(1/2)(3 + 2sqrt(3) + 1)
= -2 - sqrt(3)

Answer 2

tan 75 = tan(45+30) =(1+sqrt3/3)/(1-sqrt3/3)
tan 285 = tan(360-75) = tan(-75)=-tan75

Answer 3

1) tan 75=tan(45+30)=(tan45+tan30)/(1-tan45tan30)
=(1+1/sqrt3)/(1-1/sqrt3)
2) tan 285=tan(360-75)
=-tan75
=-tan(45+30)=(tan45+tan30)/(1-tan45tan30)
=(1+1/sqrt3)/(1-1/sqrt3)