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Prove that Cot^(-1)9+"Cosec"^(-1) (sqrt(...

Prove that `Cot^(-1)9+"Cosec"^(-1) (sqrt(41))/4 = (pi)/4`.

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AAKASH SERIES-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 7.1 ( SHORT ANSWER QUESTIONS)
  1. Show that Tan^(-1) 1/7 + Tan^(-1) 1/8 = Cot^(-1) 201/43 + Cot^(-1) 18

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  2. Prove that "Tan"^(-1)2+Tan^(-1)3=Cot^(-1)(1/2)+Cot^(-1)(1/3)=(3pi)/4

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  3. Prove that Cot^(-1)9+"Cosec"^(-1) (sqrt(41))/4 = (pi)/4.

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  4. P.T. Cos^(-1)((4)/(5))+Sin^(-1)((3)/(sqrt34))=Tan^(-1)((27)/(11)).

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  5. Show that "sec"^(2)(Tan^(-1)2)+"cosec"^(2)(Cot^(-1)2) =10

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  6. Show that Sec^(2)(cot^(-1)3)+(Cosec^(2)(tan^(-1)2))=85/36

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  7. Show that cot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3).

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  8. Show that cos(2"Tan"^(-1)1/7)=sin(4"Tan"^(-1)1/3)

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  9. sin(2"Tan"^(-1)3/4)=

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  10. Show that tan[2 tan^(-1)((sqrt(5)-1)/(2))]=2

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  11. "Tan"^(-1)1/4+"Tan"^(-1)2/9=

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  12. Prove that 2sin^-1(3/5)-Cos^-1""5/13=Cos^-1(323/325).

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  13. Prove that "Sin"^(-1)4/52"+Tan"^(-1)1/3=(pi)/2

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  14. If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)...

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  15. If Cos^(-1)p+Cos^(-1)q+Cos^(-1)r = pi then, P.T. p^(2)+q^(2)+r^(2) = 2...

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  16. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi then prove that n xsqrt(1-x^(2))+y...

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  17. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

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  18. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

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  19. tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

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  20. Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1.

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