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If sin^(-1)x1+sin^(-1)x2++sin^(-1)xnlt==...

If `sin^(-1)x_1+sin^(-1)x_2++sin^(-1)x_nlt==(npi)/2,n in N ,n=2m+1, mgeq1,` then find the value of `(x1 1+x3 3+x5 5+(m+1)t e r m s)/(x2 2+x4 4+x6 6+ mt e r m s)`

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To solve the problem, we need to analyze the given condition and derive the required expression step by step. ### Given: \[ \sin^{-1} x_1 + \sin^{-1} x_2 + \ldots + \sin^{-1} x_n \leq \frac{n\pi}{2} \] where \( n \in \mathbb{N} \) and \( n = 2m + 1 \) for \( m \geq 1 \). ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. If sin^(-1) (x^(2) + 2x + 2) + tan^(-1) (x^(2) - 3x - k^(2)) gt (pi)/(...

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  2. If cos^(-1)lambdacos^(-1)mu+cos^(-1)gamma=3pi, then find the value of ...

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  3. If sin^(-1)x1+sin^(-1)x2++sin^(-1)xnlt==(npi)/2,n in N ,n=2m+1, mgeq1...

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  4. Find x satisfying [tan^(-1)x]+[cos^(-1)x]=2, where [] represents the g...

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  5. If cos (2 sin^(-1) x) = (1)/(9), then find the value of x

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  6. Find the value of sin((1)/(2) cot^(-1) (-(3)/(4)))

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  7. Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin...

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  8. Solve sin^(-1)(1-x)-2s in^(-1)x=pi/2

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  9. Find the solutions of the equation cos(cos^-1 x) =cosec (cosec^-1x).

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  10. Find the principal values of the following (i) sin^(-1) (sin 1) (ii...

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  11. Solve sin^(-1) (sin 6x) = x, x in [0,pi]

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  12. Solve sin^(-1) [sin((2x^(2) + 4)/(1 + x^(2)))] lt pi -3

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  13. Find the area bounded by y = sin^(-1) (sin x) and x-axis for x in [0, ...

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  14. Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1)...

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  15. Find the principal value of the following (i) cos^(-1) (cos 3) (ii) ...

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  16. Solve cos^(-1) (cos x) gt sin^(-1) (sin x), x in [0, 2pi]

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  17. Find the principal values of the following (i) tan^(-1) (tan. (2pi)/...

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  18. Find the number of solution of 2 tan^(-1) (tan x) = 6 - x

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  19. Write tan^(-1) x, x gt 0 in the form of other inverse trigonometric fu...

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  20. Find tan^(-1). (x)/(sqrt(a^(2) - x^(2))) in terms of sin^(-1), where x...

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