Question

$<b>{In a right angle triangle ABC, right angle is at B, if tanA=√3 then find the value of}$

$\huge{ sin A cosC + cos A sin C}$

Answer 1

tanA = √3

A = 60

B = 90

C = 180-60-90 = 30

So Sin A Cos C + Cos A SinC

Sin ( A + C)

Sin ( 180 - B)

SinB

Sin 90

1

Answer 2

Step-by-step explanation:

Given that

tanA=

1

3

AC=

(

3

)

2

+1

2

=

3+1

=

4

=2

now

(i)sinAcosC+cosAsinC

=

2

3

×

2

3

+

2

1

×

2

1

=

4

3

+

4

1

=

4

4

=1

and

(ii)cosAcosC−sinAsinC

=

2

1

×

2

3

−

2

1

×

2

3

=

4

3

−

4

3

=0