Question

If sinθ=√53 then what is cos2θ?

Answer 1

Given that

$\sin( \alpha ) = \sqrt{53}$

$\cos(2 \alpha ) = 1 - 2 { \sin( \alpha ) }^{2}$

then

$\cos(2 \alpha ) = 1 - 2( { \sqrt{53} }^{2} )$

$\cos(2 \alpha ) = 1 - 106$

$\cos(2 \alpha ) = - 105$

we use alpha in place of thetha if you don't mind

hope am I right