How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

Answers

Answer 1

Answer: $LHS\n \n =\frac { \tan ^( 2 ){ x-\sin ^( 2 ){ x } } }{ \tan { x } } \n \n =\frac { 1 }{ \tan { x } } \left( \tan ^( 2 ){ x-\sin ^( 2 ){ x } } \right)$

$\n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x } }{ \cos ^( 2 ){ x } } -\frac { \sin ^( 2 ){ x\cos ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \right) \n \n =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^( 2 ){ x-\sin ^( 2 ){ x\cos ^( 2 ){ x } } } }{ \cos ^( 2 ){ x } } \right)$

$\n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\left( 1-\cos ^( 2 ){ x } \right) } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^( 2 ){ x\cdot \sin ^( 2 ){ x } } }{ \cos ^( 2 ){ x } } \n \n =\frac { \cos { x } \sin ^( 4 ){ x } }{ \sin { x\cos ^( 2 ){ x } } } \n \n =\frac { \sin ^( 3 ){ x } }{ \cos { x } }$

$\n \n =\sin ^( 2 ){ x } \cdot \frac { \sin { x } }{ \cos { x } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \n \n =\sin ^( 2 ){ x } \cdot \frac { 1 }{ \cot { x } } \n \n =\frac { \sin ^( 2 ){ x } }{ \cot { x } } \n \n =RHS$

Related Questions

The area, A, of a square is equivalent to the square of its side lengths. choose more than one!1::: A = (6)(6) square units2::: A = s2 square units3::: A = (x)(x) square units4::: A = (x+x) square units5::: A = 2(6) square units
Help me, please, i"m desperate
• a baseball player went up to bat 250 times in a season. he hit the ball 100 times. find the rate of balls hit to times at bat. express as a simplified fraction. 0 } 0 2 5 о
There are 35 students in Zacks class.Out of the 35,16 prefer chocolate ice cream to vanilla (46%),while 9 prefer vanilla to chocolate (26%).What does this mean?
7 copies of the sum of 8 fifths and 4

What is the measure of angle AED ?
degrees