Question

4- In triangle ABC, right-angled at B, if tan A = find the value of: 13
(i) sin A cos C + cos A sin C
(ii) cos A cos C - sin A sin C​

Answer 1

Step-by-step explanation:

Solution

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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

Answer 2

I am not poor in mathematics l