Question

Find the value of cosec^2 30 degree - sin^45 - sec^60

Answer 1

For this question, I will be writing 'csc' instead of 'cosec'

`\sin 30^(\circ)=(1)/(2) \implies \csc 30^(\circ)=2\\\\\sin 45^(\circ)=(1)/(√(2))\\\\\cos 60^(\circ)=(1)/(2) \implies \sec 60^(\circ)=2\\\\\\\therefore \csc^(2) 30^(\circ)-\sin^(2) 45^(\circ)-\sec^(2) 60^(\circ)=2^(2)-\left((1)/(√(2)) \right)^(2)-2^(2)=\boxed{-(1)/(2)}`