In which of the following sets the inequality `sin^6x+cos^6x >5/8` holds good? (a)`(-pi/3,pi/8)` (b) `((3pi)/8,(5pi)/8)` (c) `(pi/4,(3pi)/4)` (d) `((7pi)/8,(9pi)/8)`

Explanation

To solve the inequality \( \sin^6 x + \cos^6 x > \frac{5}{8} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression \( \sin^6 x + \cos^6 x \). We can use the identity for the sum of cubes:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
Let \( a = \sin^2 x \) and \( b = \cos^2 x \). Then:
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