Exercise 3 Solve the following equations for x a tan1 x sin

Exercise #3 Solve the following equations for x a) tan-1 x = sin-1 ( b) sin-1 (z-2)- c) sin+ cos d) cos-1 x + sin-T =

Solution

a)

tan^-1(x) =sin^-1(24_/25)

=> tan^-1(x) =tan^-1(24_/(25²-24²))

=> tan^-1(x) =tan^-1(24_/(625-576))

=> tan^-1(x) =tan^-1(24_/49)

=> tan^-1(x) =tan^-1(24_/7)

=> x =24_/7

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(b)

sin^-1(x-2) =(-_/6)

=>x-2=sin(-_/6)

=>x-2 =-sin(_/6)

=>x-2 =-(1_/2)

=>x =(3_/2)

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c)

sin^-1x +cos^-1(4_/5) =(_/6)

=>sin^-1x =(_/6)-cos^-1(4_/5)

=>x  =sin((_/6)-cos^-1(4_/5))

=>x  =sin(_/6)cos(cos^-1(4_/5)) -cos(_/6)sin(cos^-1(4_/5))

=>x  =(1_/2)(4_/5) -(3_/2)sin(cos^-1(4_/5))

=>x  =(1_/2)(4_/5) -(3_/2)sin(sin^-1(3_/5))

=>x  =(1_/2)(4_/5) -(3_/2)(3_/5)

=>x  =(1_/10)(4 -33)

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d)

cos^-1x +sin^-1(3_/2) =(_/2)

=>cos^-1x +(_/3) =(_/2)

=>cos^-1x =(_/2)-(_/3)

=>cos^-1x  =(_/6)

=>x  =cos(_/6)

=>x=3_/2