निम्नलिखित को साबित करे
`sin^(2)(3pi)/(4)+2 cos^(2)(pi)/(4)+2sec^(2)(pi)/(3)=10`

Explanation

(i) `sin (3pi)/(4)= sin (pi-(pi)/(4))=sin(pi)/(4)`
अब `L.H.S = 2 sin^(2)(3pi)/(4)+2 cos^(2)(pi)/(4)+2 sec^(2)(pi)/(3)`
`= 2 sin^(2)(pi)/(4)+2 cos^(2)(pi)/(4)+2 sec^(2)(pi)/(3)`
`=2 (sin^(2))(pi)/(4)+(2)^(2)=2+8=10` R.H.S
अब `L.H.S =2 sin^(2)(pi)/(6)+cosec^(pi)/(6)`
`=2(1/2)^(2)+(-cosec(pi))/(6)^(2) cos^(2) (pi)/(3)`
`=2xx1/4+cosec^(2)(pi)/(6) cos^(2)(pi)/(3)`
`=1/2+(2)^(2)(1/2)^(2)=1/2+1=3/2`= R.H.S