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P.T. Cos^(-1)((4)/(5))+Sin^(-1)((3)/(sqr...

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

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sin^(-1)((sqrt(3))/2)-tan^(-1)(-sqrt(3))=

Sin^(-1)(3/5)+Cos^(-1)(5/sqrt34)=

Cos^(-1)((-1)/2)-2Sin^(-1)(1/2)+3Cos^(-1)((-1)/sqrt(2))-4Tan^(-1)(-1)=

Cos^(-1)((-1)/2)-2Sin^(-1)(1/2)+3Cos^(-1)((-1)/sqrt2)-4Tan^(-1)(-1)=

sin^(-1)(-1/2)=tan^(-1)((-1//2)/(sqrt(1-1/4)))=tan^(-1)((-1)/(sqrt(3)))

Sin^(-1)(4/5)+2Tan^(-1)""1/3=

cos^(-1)(-1/4)=pi+tan^(-1)(-sqrt(15))

tan^(-1)(2)=sin^(-1)(2/(sqrt(5)))=cos^(-1)(1/(sqrt(5)))

cos^(-1)((-3)/4)=pi-sin^(-1)sqrt(1-9/16)=pi-sin^(-1)((sqrt(7))/4)

AAKASH SERIES-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 7.1 ( SHORT ANSWER QUESTIONS)
  1. Prove that "Tan"^(-1)2+Tan^(-1)3=Cot^(-1)(1/2)+Cot^(-1)(1/3)=(3pi)/4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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