Using cos(A + B) = cosA cosB - sinA sinB, find the value of cos75°.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. .
cos(A + B) = cosA cosB - sinA sinB
Putting A = 45° and B = 30°
cos(45° + 30°) = cos45° cos30° - sin45° sin30°
On putting the trigonometric values
⇒ cos75° = 1/√2 × √3/2 - 1/√2 × 1/2
⇒ cos75° = √3/2√2 - 1/2√2
⇒ cos75° = (√3 - 1)/2√2
on rationalize
⇒ cos75° = (√3 - 1)/2√2 × 2√2/2√2
⇒ cos75° = 2√2(√3 - 1)/8
⇒ cos75° = 2(√6 - √2)/8
⇒ cos75° = (√6 - √2)/4