If cot4 A + cot2 A = 1, then find the value of cos4 A - 3cos2 A.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. -1.
Given that
If cot4 A + cot2 A = 1
Calculation
⇒ cot4 A + cot2 A = 1
⇒ cot2 A (cot2 A + 1) = 1
⇒ cos2 A = sin4 A = (1 - cos2 A)2
⇒ cos2 A = 1 + cos4 A - 2cos2 A
⇒ cos4 A - 2cos2 A - cos2 A = -1
⇒ cos4 A - 3cos2 A = -1