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'

$\sin 30^{\circ}=\frac{1}{2} \implies \csc 30^{\circ}=2\\\\\sin 45^{\circ}=\frac{1}{\sqrt{2}}\\\\\cos 60^{\circ}=\frac{1}{2} \implies \sec 60^{\circ}=2\\\\\\\therefore \csc^{2} 30^{\circ}-\sin^{2} 45^{\circ}-\sec^{2} 60^{\circ}=2^{2}-\left(\frac{1}{\sqrt{2}} \right)^{2}-2^{2}=\boxed{-\frac{1}{2}}$