How do you verify ${tan}^{5} x = {tan}^{3} x {sec}^{2} x - {tan}^{3} x$ $tan^5 x = tan ^3 x sec^2 x - tan^3 x$ ?

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How do you verify ${tan}^{5} x = {tan}^{3} x {sec}^{2} x - {tan}^{3} x$ $tan^5 x = tan ^3 x sec^2 x - tan^3 x$ ?

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Answer 1 · 2018-03-10T15:09:32

$R H S = {tan}^{3} x \cdot {sec}^{2} x - {tan}^{3} x$ $RHS=tan^3x*sec^2x-tan^3x$

$= {tan}^{3} x ({sec}^{2} x - 1) = {tan}^{3} x \cdot {tan}^{2} x = {tan}^{5} x = L H S$ $=tan^3x(sec^2x-1)=tan^3x*tan^2x=tan^5x=LHS$

Answer 2 · 2018-03-10T15:26:03

$see explanation$ $"see explanation"$

Explanation:

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

$∙ x 1 + {tan}^{2} x = {sec}^{2} x$ $•color(white)(x)1+tan^2x=sec^2x$

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

${tan}^{5} x = {tan}^{3} x \times {tan}^{2} x$ $tan^5x=tan^3x xxtan^2x$

${tan}^{5} x = {tan}^{3} x ({sec}^{2} x - 1)$ $color(white)(tan^5x)=tan^3x(sec^2x-1)$

${tan}^{5} x = {tan}^{3} x {sec}^{2} x - {tan}^{3} x = right side$ $color(white)(tan^5x)=tan^3xsec^2x-tan^3x=" right side"$

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How do you verify ${tan}^{5} x = {tan}^{3} x {sec}^{2} x - {tan}^{3} x$ $tan^5 x = tan ^3 x sec^2 x - tan^3 x$ ?

2 Answers

Explanation:

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How do you verify tan^5 x = tan ^3 x sec^2 x - tan^3 xtan5x=tan3xsec2x−tan3xtan^5 x = tan ^3 x sec^2 x - tan^3 x?

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Explanation:

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How do you verify ${tan}^{5} x = {tan}^{3} x {sec}^{2} x - {tan}^{3} x$ $tan^5 x = tan ^3 x sec^2 x - tan^3 x$ ?