Let ABC be a right-angled triangle with a right angle at B. If tan A = √3, then find the value of sin A cos C + cos A sin C and cos A cos C - sin A sin C.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1 and 0.
Triangle ABC is right-angled at B, and tan A = √3
tan 60° = √3
⇒ A = 60°
In a right-angled triangle, the sum of the other two angles is 90°.
Since ∠B is 90° and ∠A is 60°, ∠C = 90° - 60° = 30°
Now, sin A cos C + cos A sin C
= sin (A + C)
= sin (60° + 30°)
= sin 90°
= 1
Also, cos A cos C - sin A sin C
= cos (A + C)
= cos (60° + 30°)
= cos 90°
= 0
Therefore, the required answer is 1, 0.