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Let a = sin(t) + tan(t) and b = tan(t) - sin(t).  Find (a^2 - b^2)^2/(ab).

 Dec 20, 2019
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a^2   =    sin^2(t) + 2sin(t )tan(t)  + tan^2 (t)

b^2    =   sin^2( t)  - 2sin (t)tan (t)  + tan^2( t)

a^2 - b^2 =   4sin(t)tan(t)   ⇒ (a^2 - b^2)^2  =  4sin^2(t) tan^2(t)

ab =  tan^2(t) -  sin^2 (t)

 

(a^2  - b^2)^2

_____________    = 

     ab 

 

 

4sin^2 (t) tan^2 (t)

________________       =

tan^2(t) - sin^2(t)

 

 

4 sin^2(t) sin^2(t) / cos^2(t)

_______________________________      =

[sin^2(t) - sin^2(t) cos^2(t)]  / cos^2(t)

 

 

4 sin^2(t) (sin^2(t)

____________________   =

sin^2 (t) ( 1 - cos^2(t) )

 

 

4 sIn^2(t) sin^2(t)

________________   =

sin^2(t) sin^2(t)

 

4

 

 

cool cool cool

 Dec 20, 2019

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