Question

verify-
sin(x+pi/2)=cos x
and
cos(4u)=cos^2 (2u)-sin^2 (2u)

Answer 1

Use the formula for sin(A+B)
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
sin(x+pi/2) = sin(x)cos(pi/2) + cos(x)sin(pi/2) = ?
simplify.

Answer 2

for wich one

Answer 3

oh nvm the first one

Answer 4

wouldnt the other side just turn into sin(pi/2 - x)

Answer 5

so then it would be sin( x+pi/2)=sin(pi/2-x)

Answer 6

but now i dont know what to do after this

Answer 7

sin(x+pi/2) = sin(x)cos(pi/2) + cos(x)sin(pi/2)
cos(pi/2) = 0; sin(pi/2) = 1
sin(x+pi/2) = sin(x) * 0 + cos(x) * 1 = cos(x)

Answer 8

For the second problem:
cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
cos(4u) = cos(2u + 2u). Use the above identity.
cos(2u + 2u) = cos(2u)cos(2u) - sin(2u)sin(2u) = cos^2(2u) - sin^2(2u)

Answer 9

hold on im trying to comprehend

Answer 10

For the second problem A = 2u and B = 2u in the identity cos(A+B) which makes it cos(4u).