ΔABC is a right triangle. If ∠B = 90° and tan A , then the value of sin A cos C + cos A sin C is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1.
We have,
tan A = 1/√3
Now, we can solve for the following values;
sin A = 1/2 and cos C = 1/2
cos A = √3/2 and sin C = √3/2
According to the question;
⇒ sin A cos C + cos A sin C
⇒ 1/2 × 1/2 + √3/2 × √3/2
⇒ 1/4 + 3/4
⇒ 4/4 = 1