What is the value of [sin (90° – A) + cos (180° – 2A)]/[cos (90° – 2A) + sin (180° – A)]?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. tan (A/2)
[sin (90° – A) + cos (180° – 2A)]/[cos (90° – 2A) + sin (180° – A)]
= [cosA + (-cos 2A)]/[sin2A + sinA] = (cosA - cos2A)/(sin2A + sinA)
= [{2sin(A + 2A)/2}{sin(2A - A)/2)}]/[{2sin(2A + A)/2{cos(2A - A)/2}]
= sin(A/2)/cos(A/2)
= tan(A/2)