Question

prove that:sin4theta+cos4theta+2sin2theta cos2theta=1

Answer 1

Solution

Let's understand it first,

→ a⁴ + b⁴ + 2a²b²

→ (a ²+ b²)² - 2a²b² + 2a²b²

Because (a ²+ b²)² - 2a²b² = a⁴ + b⁴ + 2a²b² - 2a²b² = a⁴ + b⁴.

(っ.❛ ᴗ ❛.)っ

Coming onto solution,

L.H.S → sin⁴∅ + cos⁴∅ + 2 sin²∅ cos²∅

→ (sin²∅ + cos²∅)² - 2 sin²∅ cos²∅ + 2 sin²∅ cos²∅

→ (sin²∅ + cos²∅)²

Since sin²∅ + cos²∅ = 1,

→ 1² = 1 = R.H.S

Q.E.D