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Discussion Response Post to: INVERSE TRIGNO-ans req soooooooooooooooooonnnnnnnnnnnnnnnnnnnn

Forum Index -> Trignometry -> View Full Question

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Titun (1467)

Forum Expert

total posts: 374
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1st problem.

0

cos ^{- 1} x

Therefore, 0

cos ^-1x ₁

cos ^-1x ₂

                         .
                         .
                         .
                         .
                         .
              0

cos ^-1x _n

Therefore,

cos ^-1x₁ + cos ^-1x₂ + ................ cos ^-1x_n

The equality holds only when

cos ^-1x₁ = cos ^-1x₂= .............................. = cos ^-1x_n =

i.e x₁ = x₂ = ..........................................= x_n= - 1

So,
x₁² + x₂² + ............................+ x_n² = 1+1+ .............n times = n

2nd problem.

-

/ 2

sin ^{- 1} x

/2

Therefore, -

sin ^-1x ₁

/2
-

sin ^-1x ₂

/2
                         .
                         .
                         .
                         .
                         .
             -

sin ^-1x _2n

/2

Therefore,

sin^-1x₁ + sin ^-1x₂ + ................ sin ^-1x_2n

2n .

/2 = n

The equality holds only when

sin ^-1x₁ = sin ^-1x₂= .............................. = sin ^-1x_2n =

/2
i.e x₁ = x₂ = ..........................................= x_2n= 1

So,
x₁ + x₂ + ............................+ x_2n = 1+1+ .............2n times = 2n

Cheers !!!!!

You never know what is enough till you know what is more than enough. Titun

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