Question

solve fast.......
fast...​

Answer 1

Answer:

To keep things neat, put x = cos θ and y = sin θ.

Then

x² + y² = 1.          ... (1)

Squaring (1) gives

1 = (x² + y²)² = x⁴ + y⁴ + 2x²y²      ... (2)

Cubing (1) gives

1 = (x² + y²)³ = x⁶ + y⁶ + 3x²y²(x² + y²) = x⁶ + y⁶ + 3x²y²     ... (3)

Now 2 times equation (3) minus 3 times equation (2) gives

2 - 3 = 2(x⁶ + y⁶ + 3x²y²) - 3(x⁴ + y⁴ + 2x²y²)

       = 2(x⁶ + y⁶) - 3(x⁴ + y⁴)  + 6x²y² - 6x²y²

       = 2(x⁶ + y⁶) - 3(x⁴ + y⁴)

=> 2(x⁶ + y⁶) - 3(x⁴ + y⁴) + 1 = 0.