in right angle triangle abc right angle is at angle C and tanA = 1/√3 then find the value of sinA cosB + cosA sinB
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tanA=
3
1
AC
BC
=
3
1
AC=
3
BC
Also, (AC)
2
+(BC)
2
=(AB)
2
3(BC)
2
+(BC)
2
=(AB)
2
AB=2BC
AB:BC:AC=2:1:
3
sinA=
AB
BC
=
2
1
cosA=
AB
AC
=
2
3
sinB=
AB
AC
=
2
3
cosB=
AB
BC
=
2
1
sinAcosB+cosAsinB=
2
1
×
2
1
+
2
3
×
2
3
=1
Also, sinAcosB+cosAsinB=sin(A+B)
In right angled ΔABC.
A+B+C=180
∘
(C=90
∘
)
A+B=90
∘
sin(A+B)=sin90
∘
=1
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