What is the value of cos 15° + cos 105°?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1/√2.
cos 15° + cos 105°
= cos 15° + cos (90 + 15)°
= cos 15° - sin 15°
= cos (45° – 30°) – sin (45° – 30°)
= [cos45° cos30° + sin45° sin30°] – [sin45° cos30° – cos45° sin30°]
= [1/√2 × √3/2 + 1/√2 × 1/2] – [1/√2 × √3/2 – 1/√2 × 1/2]
= 1/2√2 + 1/2√2
= 1/√2