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sinx/cosx × secx/cosecx × tanx/cotx =9 solve for x if x[0,pie/2]

sinx/cosx × secx/cosecx × tanx/cotx =9 
solve for x if x[0,pie/2]

Grade:11

1 Answers

Tanvir Mahmud Abir
13 Points
3 years ago
(sinx)/(cosx)*(secx)/(cosecx)*(tanx)/(cotx)=9
or, sinx*(1)/(cosx)*secx*(1)/(cosecx)*tanx*(1)/(cotx)=9
or, sinx*(1)/(cosx)*(1)/(cosx)*sinx*tanx*tanx=9
or, sinx*sinx*(1)/(cosx)*(1)/(cosx)*tanx*tanx=9
or, sin^(2)x*(1)/(cos^(2)x)*tan^(2)x=9
or, (sin^(2)x)/(cos^(2)x)*tan^(2)x=9
or, ((sinx)/(cosx))^(2).tan^(2)x=9
or, (tanx)^(2)*tan^(2)x=9
or, tan^(2)x*tan^(2)x=9
or, tan^(4)x=9
or, tanx=\root(4)(9)
or, tanx=\pm \sqrt(3)
now,
if, 
  tanx=+\sqrt(3)                        [x is in the first quadrant]
  tanx=tan(\pi )/(3)
  tanx=tan60\deg 
  x=60\deg 
 
 
if,tanx=-\sqrt(3)                         [x is in the 2nd or 4th quadrant]

in 2nd quadrant,
tanx=-tan(\pi )/(3)
tanx=tan(\pi -(\pi )/(3))
tanx=tan((2\pi )/(3))
tanx=tan120\deg 
x=120\deg                                [but 0
so x is not equal to 120\deg 

in 4th quadrant,
tanx=-tan(\pi )/(3)
tanx=tan(2\pi -(\pi )/(3))
tanx=tan((5\pi )/(3))
tanx=tan300\deg 
x=300\deg                                [but 0
so x is not equal to 300\deg 
so x=60\deg  (ans)

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