Question

Q. In triangle ABC, right angled at B , if tan A =1/√3 , find the value of :. 1) sin A cosC +cos a. sin c. 2) cos a cos c + sin a sin c.​

Answer 1

Answer:

Given that :

tan A = $\sf{\frac{1}{\sqrt{3}}}$

Now, the value of tan A is $\sf{\frac{1}{\sqrt{3}}}$ when the angle is equal to 30°

$\sf{\therefore}$/_$\sf{A = 30\degree}$

We already know that /_B = 90°

Now, we've found that /_A = 30°

By the Angle Sum Property, we can find that /_C = 60°

Now the solutions:-

Solution of Part 1

=》 sin A cos C + cos A sin C

=》 $\tt{\frac{1}{2}\times \frac{1}{2} + \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2}}$

=》 1

__________

Solution of Part 2

=》 cos A cos C + sin A sin C

=》 $\tt{\frac{\sqrt{3}}{2}\times \frac{1}{2} + \frac{1}{2} \times \frac{\sqrt{3}}{2}}$

=》 $\tt{\frac{\sqrt{3}}{2}}$

=》 sin 60°

Answer 2

Answer:

1) 1

2) √3/2

Step-by-step explanation:

tan30° = 1/√3

tanA = tan30°

A = 30°

B = 90°

C = 60°

Sin30°*Cos60° + Cos30°*Sin60° = Sin(30 + 60) = 1

Cos30*Cos60 + Sin30*Sin60 = Cos (30 - 60) = √3/2