MCQ
Let $f(x) = \left| {\begin{array}{*{20}{c}}{\,\sec x}&{\cos x}&{{{\sec }^2}x + \cot x\,{\rm{cosec}}\,x\,}\\{{{\cos }^2}x}&{{{\cos }^2}x}&{{\rm{cose}}{{\rm{c}}^2}x}\\1&{{{\cos }^2}x}&{{{\cos }^2}x}\end{array}} \right|\,,$ then $\int_0^{\pi /2} {\,f(x)\,dx = } $
- A$\frac{\pi }{4} + \frac{8}{{15}}$
- B$\frac{\pi }{4} - \frac{8}{{15}}$
- ✓$ - \frac{\pi }{4} - \frac{8}{{15}}$
- D$ - \frac{\pi }{4} + \frac{8}{{15}}$