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

1.	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» (c) \(\frac{47}{24}\) Given exp. = \(\bigg(\frac12\bigg)^2\times\bigg(\frac1{\sqrt2}\bigg)^2+4\times\bigg(\frac1{\sqrt3}\bigg)^2+\frac12\times(1)^2-2\times0\) = \(\frac14\times\frac12+4\times\frac13+\frac12=\frac18+\frac43+\frac12=\frac{3+32+12}{24}=\frac{47}{24}\)

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»

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

Given exp.

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

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