Question

prove that
$\sec^{4} theta \: - \cos^{4} theta \: = 1 - 2 \cos^{2} theta$
​

Answer 1

Step-by-step explanation:

LHS = sin⁴θ - cos⁴θ

=(sin² θ)² - (cos² θ) ²

=(sin²θ - cos² θ) (sin²θ + cos²θ )

..[a²-b² = (a + b)(a - b)]

= sin²θ - cos²θ ..(sin²θ + cos²θ= 1)

= 1 - cos²θ - cos²θ ..(sin²θ = 1 - cos²θ)

= 1 - 2 cos²θ

= RHS