If tan (A+B) = 3 and tan (A-B)= J :0° <A+B<90; A > B, find A and B.
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Given:-
๛Tan(A+B)=√3
๛Tan(A-B)=0
ToFind:-
➜The Value of Sin(A+B) and Cos(A-B)?
AnsWer:-
☞Cos0°=1
☞Sin60°=
[°•°Tan60°=√3]
↝Tan(A+B)=Tan60
↝A+B=60-(1)
[°•°Tan0°=0]
↝Tan(A-B)=Tan0
↝A-B=0-(2)
✪Add (1)&(2)✪
↝A+B=60
↝A-B=0
★Signs Changed★
↝2A=60
\frac{\cancel{60}}{\cancel{2}}
↝B=
☞B=30-(3)
✪Using (3) in (2)✪
↝A-30=0
↝A=30-(4)
✪Using (4) and (3) for Sin(A+B)✪
↝Sin(A+B)=Sin(30+30)
☞Sin60°=
\frac{\sqrt{3}}{2}
✪Using (4) and (3) for Cos(A-B)✪
↝Cos(A-B)=Cos(30-30)
☞Cos0=1
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