Question #923f4

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Answer 1 · 2017-03-23T02:08:12

I tried this:

If you multiply the brackets you get:

$1cancel(+sin(x))cancel(-sin(x))-sin^2(x)=cos^2(x)$

$1-sin^2(x)=cos^2(x)$ that it is true;

remembering the fundamental identity:
$sin^2(x)+cos^2(x)=1$

Answer 2 · 2017-03-24T00:56:07

$"Given: "(1-sinx)(1+sinx)=cos^2x$

$"LHS"=(1-sinx)(1+sinx)$

$=1+sinx-sinx-sin^2x$

$=1-sin^2x$

Use the Pythagorean identity: $color(blue)(sin^2x+cos^2x=1)$

$color(blue)(cos^2x=1-sin^2x)$

$"LHS"=cos^2x$

$"QED"$