The value of 1/2 sin^2 90° sin^2 30° cos^2 45° + 4 tan^2 30° + 1/2 sin^2 90° – 2 cos^2 90° is:

Question

The value of \(\frac12\) sin² 90° sin² 30° cos² 45° + 4 tan² 30° + \(\frac12\) sin² 90° – 2 cos² 90° is:

(a) \(\frac{45}{24}\)

(b) \(\frac{46}{24}\)

(c) \(\frac{47}{24}\)

(d) \(\frac{49}{24}\)

Answer 1

(c) \(\frac{47}{24}\)

Given exp.

= \(\bigg(\frac12\bigg)^2\times\bigg(\frac1{\sqrt2}\bigg)^2+4\times\bigg(\frac1{\sqrt3}\bigg)^2+\frac12\times(1)^2-2\times0\)

= \(\frac14\times\frac12+4\times\frac13+\frac12=\frac18+\frac43+\frac12=\frac{3+32+12}{24}=\frac{47}{24}\)