If cos²Θ – sin²Θ = x, then 1 + cos⁴Θ – sin⁴Θ = ?

A x

B 4/x

C x + 1

D x² + 1

Solution

Correct Answer: Option C

We know,
cos²Θ + sin²Θ = 1
and, cos²Θ - sin²Θ = x
Now, (cos²Θ + sin²Θ) × (cos²Θ - sin²Θ) = 1 × x
⇒ cos⁴Θ - sin⁴Θ = x
⇒ 1+ cos⁴Θ - sin⁴Θ = 1+ x = x + 1

If cos2Θ – sin2Θ = x, then 1 + cos4Θ – sin4Θ = ?

Solution

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If cos²Θ – sin²Θ = x, then 1 + cos⁴Θ – sin⁴Θ = ?