1.

Evaluate : `(2sin^2 63^@+1+2sin^2 27^@)/(3 cos ^2 17^@-2+3cos^2 73^@)`

Answer» Given exrpession
`(2sin^2 63^@+1+2sin^2 27^@)/(3 cos ^2 17^@-2+3cos^2 73^@)=(2(sin^2 63^@+sin^2 27^@)+1)/(3(cos^2 17^@+cos^2 73^@)-2)`
`=(2[sin^2 63^@+sin^2 (90^@-63^@)]+1)/(3[cos^2 17^@+cos^2 (90^@-17^@)]-2)`
`=(2[sin^2 63^@+cos^2 63^@]+1)/(3[cos^2 17^@+sin^2 17^@]-2)`
`[because sin (90^@-theta)=cos theta and cos (90^@-theta )=sin theta ]`
`=((2xx1)+1)/((3xx1)-2)=(2+1)/(3-2)=(3)/(1)=3`.


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