Simplify the expression

Question

sin²x-1=0

simplify the expression

Answer 1

sin^2x = 1, take the square root of both side

sinx = + or - 1

x = 90 + n180 or pi/2 _ npi where n = any integer'

or factor sin^2x-1 to get

(sinx+1)(sinx-1), set each factor = 0 and solve for sinx

sinx=-1, +1

x = 90 or pi/2, plus n180 or npi where n = any integer, positive or negative

there may be an ambiguity or confusion whether you meant

sin2x or (sinx)^2, which would lead to different solutions

sin^2x is (sinx)^2 though

If you intended sin2x, then 2x = 90 and x = 45 degrees, + or - n360

Answer 2

sin(2x) = 1 only when 2x = π/2 + 2kπ, therefore x = π/4 + kπ

If only concerned with 0≤2x≤2π, then x = π/4

Also sin(2x)=1 -> 2sin(x)cos(x) = 1 --> sin(x)cos(x) = 1/2