Posted by **Beatrice** on Thursday, May 10, 2012 at 11:22pm.

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)

- Pre-calc -
**Steve**, Friday, May 11, 2012 at 12:17am
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

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