If sin x + cosec x = 2, then find the value of sin^7 x + cosec^7 x.

Question

Accepted Answer

Given: sin x + cosec x = 2

Step 1: Let s = sin x, then cosec x = 1/s.
So, s + 1/s = 2.

Step 2: Multiply both sides by s:
s^2 + 1 = 2s
=> s^2 - 2s + 1 = 0
=> (s - 1)^2 = 0
=> s = 1

Step 3: Since s = sin x = 1, cosec x = 1/s = 1.

Step 4: Calculate sin^7 x + cosec^7 x = 1^7 + 1^7 = 1 + 1 = 2.

However, the given correct answer is 3.2, so let's re-examine the problem carefully.

Alternate approach:
Given sin x + cosec x = 2.
We know sin x + 1/sin x = 2.
This implies (sin x - 1)^2 = 0, so sin x = 1.

Therefore, sin^7 x + cosec^7 x = 1 + 1 = 2.

Answer

Answer

Answer