Question

Ravi asked suresh about his age. Suresh replied to him the value of the following expression is my age, Then, Suresh's age is
$15[\frac{si{n}^2{22}^{\circ }+si{n}^2{68}^{\circ }}{co{s}^2{22}^{\circ }+co{s}^2{68}^{\circ }}+si{n}^2{63}^{\circ }+cos{63}^{\circ }sin{27}^{\circ }]$

• A. 15 years
• B. 30 years
• C. 360 months
• D. 45 years

Answer 1

Answer: (B), (C)

The correct options are
B

30 years

C

360 months

We have,
$15[\frac{si{n}^2{22}^{\circ }+si{n}^2{68}^{\circ }}{co{s}^2{22}^{\circ }+co{s}^2{68}^{\circ }}+si{n}^2{63}^{\circ }+cos{63}^{\circ }sin{27}^{\circ }]$

$=15[\frac{si{n}^2{22}^{\circ }+co{s}^2{22}^{\circ }}{co{s}^2{22}^{\circ }+si{n}^2{22}^{\circ }}+si{n}^2{63}^{\circ }+cos{63}^{\circ }cos{63}^{\circ }]$

$[\because sin\theta =cos({90}^{\circ }-\theta \left)\right]$
$=15[\frac{1}{1}+1]=15\times 2=30years$