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

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

Text Solution

Verified by Experts

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.
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