Question

`2sin^(2)(3pi)/(4) + 2cos^(2)pi/4+2sec^(2)pi/3=10`

Answer 1

LHS `=2sin^(2)(3pi)/(4) + 2cos^(2)(pi/4)+2sec^(2)pi/3`
`=2[sin^(2)(3pi)/(4)+cos^(2)pi/4+sec^(2)pi/3]`
`=2[sin^(2)(pi-pi/4)+cos^(2)pi/4+sec^(2)pi/3]`
`=2[(sin^(2)pi/4+cos^(2)pi/4)+sec^(2)pi/3)]`
`=2[1+(sec 60^(@))^(2)]=2[1+2^(2)]`
`=2(1+4)=10`= RHS Hence Proved.