Is it true that (1-cos^2x)=((1+cosx)(1-cosx)?

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Answer 1 · 2018-05-08T19:31:16

Yes,it is true.

Here,

$(1 - {cos}^{2} x) = (1 + cos x) (1 - cos x)$ $(1-cos^2x)=(1+cosx)(1-cosx)$

We know that,

$(a - b) (a + b) = a^{2} - b^{2}$ $(a-b)(a+b)=a^2-b^2$

So,

$R H S = (1 - cos x) (1 + cos x)$ $RHS=(1-cosx)(1+cosx)$

$R H S = {(1)}^{2} - {(cos x)}^{2}$ $RHS=(1)^2-(cosx)^2$

$R H S = 1 - {cos}^{2} x$ $RHS=1-cos^2x$

$R H S = L H S$ $RHS=LHS$