Find the value of `[(sin^2 2 2^(@)+sin^2 6 8^(@))/(cos^2 2 2^(@)+cos^2 6 8^(@))+sin^2 6 3^(@)+cos6 3^(@)sin2 7^(@)]`

Options

A. 3
B. 2
C. 1
D. 0

Answer

B

Explanation

Given, expression , `((sin^(2)22^(@)+sin^(2)68^(@))/(cos^(2)22^(@)+cos^(2)68^(@))+sin^(2)63^(@)+cos63^(@)sin27^(@))`
`(sin^(2)22^(@)+sin^(2)(90^(2)-22^(@)))/(cos^(2)(90^(@)-68^(@))+cos^(2)68^(@))+sin^(2)63^(@)+cos63^(@)sin(90^(@)-63^(@))`
`(sin^(2)22^(@)+cos^(2)22^(@))/(sin^(2)68^(@)+cos^(2)68^(@))+sin^(2)63^(@)+cos63^(@).cos63^(@) [therefore sin(90^(@)-theta)=costheta "and" cos(90^(@)-theta)=sintheta]`
`=1/2+(sin^(2)63^(@)+cos^(2)63^(@))` `[therefore sin^(2)theta+cos^(2)theta=1]`
`1+1=2`