Question

solve this maths question​

Answer 1

Answer:

(B) 0

The restiction on θ seems to be trying to exclude this option, but this appears to be the only option possible, so we must just have to accept that θ > 90° or θ < 0°.

Step-by-step explanation:

To make the algebra clearer, let's write x = cos θ and y = sin θ.

Immediately, this rules out option (D) since -1 ≤ x ≤ 1 and -1 ≤ y ≤ 1, so 0 ≤ x²y² ≤ 1.

Now

    x² + y² = 1       ... (1)

and we are given also that

    x⁸ + y⁸ = 1.      ... (2)

Raising equation (1) to the power of 4 gives

1 = ( x² + y² )⁴ = x⁸ + 4x⁶y² + 6x⁴y⁴ + 4x²y⁶ + y⁸.

Using (2), this becomes

4x⁶y² + 6x⁴y⁴ + 4x²y⁶ = 0

=> 2x⁶y² + 3x⁴y⁴ + 2x²y⁶ = 0

=> x²y² ( 2x⁴ + 3x²y² + 2y⁴ ) = 0

=> x²y² ( 2 ( x⁴ + 2x²y² + y⁴ ) - x²y² ) = 0

=> x²y² ( 2 ( x² + y² )² - x²y² ) = 0

=> x²y² ( 2 - x²y² ) = 0

=> x²y² = 0  OR  x²y² = 2

We have already seen that x²y² ≤ 1, so x²y² = 0 is the only possibility.