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Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x...

Prove that: `tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2\ cos^(-1)x ,\ \ 0

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Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x+sqrt(1-x)))]=(pi)/(4)-(1)/(2)cos^(-1)x,quad -(1)/(sqrt(2))<=x<=1

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-TRIGONOMETRIC FUNCTIONS -Examples for Practise
  1. In any triangle ABC, prove that a(cosB+cot(A/2).sinB)=b+c.

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  2. In any triangle ABC, prove that a sin A-b sin B -=c sin (A-B).

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  3. In triangle ABC, if angle C=(pi)/(2) , then prove sin(A-B)=(a^2-b^2)/(...

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  4. In a triangle A B C , if acosA=bcosB , show that the triangle is eithe...

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  5. In a triangle ABC, prove that cot(A/2)+cot(B/2)+cot(C/2)=((a+b+c)/(b+...

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  6. In traingle ABC , prove that cos ((A-B)/(2))=((a+b)/(c)sin.(C)/(2).

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  7. Find the principal of : (1) sin ^(-1)((1)/(2)) (2) tan^(-1)(-sqrt(3)...

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  8. Find the values of : (1) cos^(-1)((1)/(2))+tan^(-1)((1)/sqrt(3)) (...

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  9. Find the value of : (1) sin^(-1)(sin.(5pi)/(6)) (2) cos^(-1)(cos.(...

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  10. Show that tan^(-1)[(cosx+sinx)/(cosx-sinx)]=(pi)/(4)+x.

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  11. सिद्ध कीजिए कि tan^(-1)""(1)/(2)+tan^(-1)""(2)/(11)=tan^(-1)""(3)/(4)

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

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  13. Evaluate : tan^(-1)1+tan^(-1)2+tan^(-1)3.

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  14. Prove that : tan^(-1)1/5+tan^(-1)1/7+tan^(-1)1/3+tan^(-1)1/8=pi/4

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  15. Prove that sin^(- 1)(8/17)+sin^(- 1)(3/5)=sin^(- 1)(77/85)

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  16. Prove that:cos^(-1)(12)/(13)+sin^(-1)3/5=sin^(-1)(56)/(65)

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  17. Prove that:2sin^(-1)3/5=tan^(-1)(24)/7

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  18. Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4...

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  19. If tan^(-1)((x-1)/(x-2))+cot^(-1)((x+2)/(x+1))=(pi)/(4) , find x.

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  20. If tan^(-1)(2x)+tan^(-1)(3x)=(pi)/(4), then find the value of x.

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