Math, asked by subhashshrma123, 10 months ago


tan2 x – sin2x = tan2 x sin2 x​

Answers

Answered by jainishpjain
0

We have to prove that (tan x)^2 - (sin x)^2 = (tan x)^2 * (sin x)^2

Start from the left hand side:

(tan x)^2 - (sin x)^2

use tan x = sin x / cos x

(sin x)^2/(cos x)^2 - (sin x)^2

=> [(sin x)^2 - (sin x)^2*(cos x)^2]/(cos x)^2

=> (sin x)^2[1 - (cos x)^2]/(cos x)^2

=> (sin x)^2 * [(sin x)^2 / (cos x)^2]

=> (tan x)^2 * (sin x)^2

which is the right hand side.

This proves that (tan x)^2 - (sin x)^2 = (tan x)^2 * (sin x)^2

HOPE THIS HELPS PLZ MARK AS BRAINLIEST

Answered by sanketj
0

RHS

 =  {tan}^{2} x \:  {sin}^{2} x \\  =  \frac{ {sin}^{2}x }{ {cos}^{2}x } . {sin}^{2} x \\  =  \frac{ {sin}^{4}x }{ {cos}^{2} x}

LHS

 =  {tan}^{2} x -  {sin}^{2} x \\  =  \frac{ {sin}^{2} x}{ {cos}^{2} x}  -  {sin}^{2} x \\  =  \frac{ {sin}^{2} x -  {sin}^{2}x \:  {cos}^{2}  x}{ {cos}^{2}x }  \\  =  \frac{ {sin}^{2} x(1 -  {cos}^{2}x) }{ {cos}^{2}x }  \\  =  \frac{ {sin}^{2}x \:  {sin}^{2}x  }{ {cos}^{2} x}  \:  \:  \:  \:  \:  \:  \: ... \: ( {sin}^{2} x +  {cos}^{2} x = 1) \\  =  \frac{ {sin}^{4} x}{ {cos}^{2}x }

= RHS

since, LHS = RHS

hence,

 {tan}^{2} x -  {sin}^{2} x =  {tan}^{2} x \:  {sin}^{2} x

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