Question

In a right angled triangle ABC, right angle is at B. If tanA= 53, then find the value of
(i) sin A cos C + cos A sin C
(ii) cos A cos C-sin A sin C​

Answer 1

Answer

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