Question

prove that 1-cos5x= 1-(1-sin^2 5x/2)

Answer 1

any one answer this please

Answer 2

Note that, by the cosine subtraction formula:
cos(A - B) = cos(A)cos(B) + sin(A)sin(B).

So, we have:
LHS = 1 - cos(5x)cos(3x) - sin(5x)sin(3x)
= 1 - [cos(5x)cos(3x) + sin(5x)sin(3x)], by factoring out the negative
= 1 - cos(5x - 3x), by the above
= 1 - cos(2x)
= 1 - [1 - 2sin^2(x)], by the double angle formula for cosine
= 2sin^2(x)
= RHS.