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Write tan^(-1) x, x gt 0 in the form of ...

Write `tan^(-1) x, x gt 0` in the form of other inverse trigonometric function

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To express \( \tan^{-1} x \) (where \( x > 0 \)) in terms of other inverse trigonometric functions, we can follow these steps: ### Step 1: Set up the relationship Let \( \theta = \tan^{-1} x \). By the definition of the inverse tangent function, we have: \[ \tan \theta = x \] ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. Find the principal values of the following (i) tan^(-1) (tan. (2pi)/...

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

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

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

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  5. Prove that sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0

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  6. If x<0, then prove that cos^(-1)x=pi-sin^(-1)sqrt(1-x^2)

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  7. Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x l...

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  8. Prove that tan^(-1) {(x)/(a + sqrt(a^(2) - x^(2)))} = (1)/(2) sin^(-1)...

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  9. Prove that sin^(-1) {(sqrt(1 + x) + sqrt(1 - x))/(2)} = (pi)/(4) + (co...

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  10. Prove that cos^(-1) ((1 - x^(2n))/(1 + x^(2n))) = 2 tan^(-1) x^(n), 0 ...

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  11. If x in [-1, 0], then find the value of cos^(-1) (2x^(2) - 1) - 2 sin^...

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  12. If (1)/(sqrt2) lt x lt 1, then prove that cos^(-1) x + cos^(-1) ((x + ...

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  13. Find the value of sin^(-1) (sin 5) + cos^(-1) (cos 10) + tan^(-1) {tan...

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  14. Find the minimum value of the function f(x) = (pi^(2))/(16 cot^(-1) (-...

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  15. Find the range of y = (cot^(-1) x) (cot^(-1) (-x))

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  16. The value of 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) is equal t...

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  17. Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2)...

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  18. If sin^(-1) x = pi//5, for some x in (-1, 1), then find the value of c...

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

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  20. solve sin^(-1) x le cos^(-1) x

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