How do you verify ${tan}^{2} x - {tan}^{2} x \cdot {sin}^{2} x = {sin}^{2} x$ $tan^2x-tan^2x*sin^2x=sin^2x$ ?

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How do you verify ${tan}^{2} x - {tan}^{2} x \cdot {sin}^{2} x = {sin}^{2} x$ $tan^2x-tan^2x*sin^2x=sin^2x$ ?

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Answer 1 · 2018-04-08T07:44:04

Please see below.

Explanation:

${tan}^{2} x - {tan}^{2} x \cdot {sin}^{2} x$ $tan^2x-tan^2x*sin^2x$

= ${tan}^{2} x (1 - {sin}^{2} x)$ $tan^2x(1-sin^2x)$

= ${tan}^{2} x {cos}^{2} x$ $tan^2xcos^2x$

= $\frac{{sin}^{2} x}{{cos}^{2} x} \cdot {cos}^{2} x$ $sin^2x/cos^2x*cos^2x$

= ${sin}^{2} x$ $sin^2x$

Answer 2 · 2018-04-08T08:04:16

$see explanation$ $"see explanation"$

Explanation:

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

$∙ x tan x = \frac{sin x}{cos x}$ $•color(white)(x)tanx=sinx/cosx$

$∙ x {sin}^{2} x + {cos}^{2} x = 1$ $•color(white)(x)sin^2x+cos^2x=1$

$consider the left side$ $"consider the left side"$

$take out a common factor {tan}^{2} x$ $"take out a common factor "tan^2x$

${tan}^{2} x (1 - {sin}^{2} x)$ $tan^2x(1-sin^2x)$

$=sin^2x/cancel(cos^2x)xxcancel(cos^2x)$

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

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How do you verify ${tan}^{2} x - {tan}^{2} x \cdot {sin}^{2} x = {sin}^{2} x$ $tan^2x-tan^2x*sin^2x=sin^2x$ ?

2 Answers

Explanation:

Explanation:

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How do you verify tan^2x-tan^2x*sin^2x=sin^2xtan2x−tan2x⋅sin2x=sin2xtan^2x-tan^2x*sin^2x=sin^2x?

2 Answers

Explanation:

Explanation:

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How do you verify ${tan}^{2} x - {tan}^{2} x \cdot {sin}^{2} x = {sin}^{2} x$ $tan^2x-tan^2x*sin^2x=sin^2x$ ?