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Find the principal values of the foll...

Find the principal values of the following :
(i) `sin^(-1)(sqrt(-3/2))`
(ii) `cot^(-1)(-sqrt(3))`
(iii) `cos^(-1)(-1(1)/(2))`
(iv) `sec^(-1)(-(2)/sqrt(3))`
(v) `tan^(-1)(-1)`
(vi) `cosec ^(-1)(-1)`.

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NAGEEN PRAKASHAN ENGLISH-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2a
  1. Find the principal values of the following : (i) sin^(-1)(sqrt(-3...

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  2. Find the principal values of the following : (i) sin^(-1)(sqrt(3)...

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  3. Find the principal values of the following : (i) sin^(-1)(sin.(5...

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  4. If cos^(-1) x = (pi)/(3), the find the value of sin ^(-1)x.

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  5. If tan ^(-1).(3)/(4)=x, the find the value of sec x.

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  6. (i) Evaluate : sec (cos^(-1).(1)/(2)) (ii) slove the equations si...

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  7. (i) If sin ^(-) x + sin ^(-1) y = pi//2, then prove that : cos^(-1) x...

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  8. If sin ^(-1) x=(1)/(3), then evaluate sin ^(-1) (2xsqrt(1-x^(2)))

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  9. prove that: 2 tan ^(-1).(1)/(3) + tan^(-1).(1)/( 7) = (pi)/(4)

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  10. Prove that: tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  11. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4; m^(2)/n^(2) > -1

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  12. Prove that : tan^(-1).(x)/(x+1)- tan ^(-1) (2x +1) = (3pi)/(4)

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  13. Prove that : tan^(-1)1/2+tan^(-1)1/5+tan^(-1)1/8=pi/4

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  14. Prove that : cot^(-1) 3 + cot^(-1).(3)/(4) = cot^(-1) .(1)/(3)

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  15. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  16. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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  17. 4tan^(- 1)(1/5)=tan^(- 1)(1/70)-tan^(- 1)(1/99)+pi/4

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  18. Prove that : cos ^(-1) ((1- a^(2))/(1+a^2)) + cos ^(-1)((1-b^(2))/(1...

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  19. tan[1/2 sin^(-1)((2a)/(1+a^2)) + 1/2 cos^(-1)((1-a^2)/(1+a^2))]=

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  20. Prove that : cos^(-1).(3)/(5)+ cos^(-1).(12)/(13) = sin^(-1)((63)/(65...

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