Question

√128*Cos^2*3Π/8-√32=?

Answer 1

8√2*(1+сos3π/4) /2 -4√2=4√2(1-√2/2) -4√2=4√2(1-√2/2-1)=4√2*(-√2/2)=-4

Answer 2

$\sqrt{128} cos ^{2} \frac{3 \pi }{8} - \sqrt{32} = \sqrt{32} ( \sqrt{4} cos ^{2} \frac{3 \pi }{8} -1)=\sqrt{32} ( 2 cos ^{2} \frac{3 \pi }{8} -1)= \\ \sqrt{32}cos(2* \frac{3 \pi }{8} )=\sqrt{32}cos\frac{3 \pi }{4} = \sqrt{32} * (-\frac{ \sqrt{2} }{2} )=-4$