Question

Convert to a product: cos(2α− pi/16 )+ cos( 9π/16 −2α) im able to get to 2cos(pi/4)*cos(4a-10pi/16) but i dont know how to simplify it even mor

Answer 1

Explanation:

`cos (2\alpha -\pi /16)+cos (9\pi/16-2\alpha )\\=2 cos (2\alpha-(\pi)/(16) +(9 \pi)/(16)-2\alpha )/(2) cos (2\alpha-(\pi)/(16)-(9 \pi)/(16)+2\alpha )/(2) \\=2cos (8 \pi)/(32) cos (4 \alpha -(10 \pi)/(16) )/(2) \\=2 cos (\pi)/(4) cos (2\alpha -(5 \pi)/(16) )\\=2 * (√(2) )/(2) cos (2\alpha -(5 \pi)/(16) )`

`=√(2) cos(2\alpha -(5 \pi)/(16) )`