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

Solve `sin^(-1)(1-x)-2sin^(-1)x=pi/2`

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To solve the equation \( \sin^{-1}(1-x) - 2\sin^{-1}(x) = \frac{\pi}{2} \), we can follow these steps: ### Step 1: Rearranging the Equation Start by isolating \( \sin^{-1}(1-x) \): \[ \sin^{-1}(1-x) = \frac{\pi}{2} + 2\sin^{-1}(x) \] ...
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Find the value of sin(1/4cos^(-1)((-1)/9))

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

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  3. Solve sin^(-1)(1-x)-2sin^(-1)x=pi/2

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  4. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  5. Simplify sincot^(-1)tancos^(-1)x , x >0

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  6. Find tan^(-1)x/(sqrt(a^2-x^2)) in terms of sin^(-1) where x in (0, a)d...

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  7. If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n th...

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  8. If 2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is independent of x , then x >1 (b...

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  9. Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by (a) exactly one ...

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  10. If the equation2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0 has ...

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  11. Let alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/...

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  12. If Sn=cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+cot^(-1)(21)+ddotn terms, ...

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  13. The value of tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 7/(16) (...

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  14. If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...

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  15. The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a...

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  16. The value of cot(sum(n=1)^2 cot^-1(1+sum(k=1)^n 2k)) is (a) 23/25 (b) ...

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  17. sin^(-1)(sin5)> x^2-4x hold if (a) x=2-sqrt(9-2pi) (b) x=2+s...

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  18. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  19. If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8))=alpha,alpha is cons...

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  20. If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equ...

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