if triangle abc is a right angled triangle with A=90 and if tan b=√3 find sin b cos c+ cos b sin c
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In △ABC,
∠B=90
o
, tanA=
3
1
=
AB
BC
Let BC =1x,AB=
3
x
AC
2
=AB
2
+BC
2
AC
2
=(
3
x)
2
+(x)
2
=4x
2
AC=2x
(i) sinAcosC+cosAsinC=
2
1
×
2
1
+
2
3
×
2
3
=
4
1
+
4
3
=1
(ii) cosAcosC−sinAsinC=
2
3
×
2
1
−
2
1
×
2
3
=
4
3
−
4
3
=0
shonaansari7876:
hii
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