Verify this identity. How would you prove it

(sin^3(x)+cos^3(x))÷(1-2cos^2(x)) = (sec(x)-sin(x))÷(tan(x)-1)

1 answer

on the LS,

sin^3+cos^3 = (sin+cos)(sin^2 - sin*cos + cos^2) = (sin+cos)(1-sin*cos)
1-2cos^2 = sin^2-cos^2 = (sin+cos)(sin-cos)

divide, giving (1-sin*cos)/(sin-cos)

on the RS,

sec-sin = 1/cos - sin = (1-sin*cos)/cos
tan-1 = sin/cos - 1 = (sin-cos)/cos

divide, giving (1-sin*cos)/(sin-cos)

LS = RS
Similar Questions
  1. verify the identitysin x(1 - 2 cos^2 x + cos^4 x) = sin^5 x 1-2cos^2 x looks like 2cos^2x-1 its just backwards. I am not sure
    1. answers icon 1 answer
    1. answers icon 1 answer
  2. How do I do these problems?Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1 - sin a)= cos^2a 2. cos^2b - sin^2b
    1. answers icon 2 answers
  3. Verify Identity:cos5x-cos3x=-8sin^2x(2cos^3x-cosx)
    1. answers icon 1 answer
more similar questions