Question

in triangle abc, angle b is equal to 90°, and tan= √3.wt is the value of CosA × Cos C - SinA × SinC​

Answer 1

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
​

​