Prove 2 cos x 4 cosx sinx Prove cot x y cotx coty 1 c

Prove: 2 cos (x + /4) = cosx - sinx

Prove: cot (x + y) = (cotx coty - 1) / (coty + cotx)

Solution:(a)

2 cos(x + /4)

use identity;

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

2 cos(x + /4) =

= 2 {cos(x) cos(/4) - sin(x) sin(/4)}

= 2 {cos(x) (1/2) - sin(x) (1/2)}

= cos(x) - sin(x) Hense Prove.

Solution:(b)

cot (x+y) = cos (x+y)/sin (x+y)

= (cos x cosy - sin x sin y)/( sin x cos y + cos x sin y)

devinding bth numberator and denominator by sin x sin y, we get;

= (( cos x/ sin x) ( cos y/ sin y) - 1)/( (cos y/ sin y) + ( cos x / sin x))

= (cot x cot y-1) /( cot y + cot x)