How do you verify $(1+cosx)(1-cosx) = sin^2 x$ ?

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How do you verify $(1+cosx)(1-cosx) = sin^2 x$ ?

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Answer 1 · 2018-07-27T14:46:37

See proof below

Explanation:

Notice, $\sin^2x+\cos^2x=1$

Now, consider LHS, as follows

$LHS=(1+\cos x)(1-\cos x)$

$=1^2-(cos x)^2$

$=1-\cos^2x$

$=\sin^2 x$

$=RHS$

Proved.

Answer 2 · 2018-07-27T19:13:07

$"see explanation"$

Explanation:

$"using the "color(blue)"trigonometric identity"$

$•color(white)(x)sin^2x+cos^2x=1$

$"consider the expansion of the left side"$

$1cancel(-cosx)cancel(+cosx)-cos^2x$

$=1-cos^2x$

$=sin^2x=" right side "rArr"verified"$

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How do you verify $(1+cosx)(1-cosx) = sin^2 x$ ?

2 Answers

Explanation:

Explanation:

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How do you verify (1+cosx)(1-cosx) = sin^2 x(1+cosx)(1-cosx) = sin^2 x?

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How do you verify $(1+cosx)(1-cosx) = sin^2 x$ ?