Prove
that
2 cos (A +45°) cos (B-45°) = cos 2A

Step-by-step explanation:

2 cos(A+45)cos (B-45)

=2[cos A cos 45-sin A sin 45][cos B cos 45+sin B sin 45]

=2[cos A ×1/√2-sin A ×1/√2][cos B×1/√2+sin B×1/√2]

=2[1/√2(cos A-sin A)][1/√2(cos B-sin B]

=2×1/√2×1/√2 (cos A-sin A)(cos B+sin B)

=cosA cos B+cos A sin B-sin A cos B-sin A sin B

=cos A cos B-sin A sin B-(sin A cos B-cos A sin B)

=cos (A+B)-sin (A-B)

i think there should be A in place of B.

then

=cos (A+A)-sin (A-A)

=cos 2A-sin 0

=cos 2A

as sin 0=0

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: