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If cos^(-1)x >sin^(-1)x , then 1/(sqrt(2...

If `cos^(-1)x >sin^(-1)x` , then `1/(sqrt(2))0`

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`cos^(-1)x >sin^(-1)x`
`cos^(-1)x >pi/2-cos^(-1)x.....`
`sin^(−1)x+cos^(−1)x=pi/2`
`2cos^(-1)x >pi/2`
`cos^(-1)x >pi/4`
`x (`cos theta` is a decreasing function).
...
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If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

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

Let g(x)=sqrt(sin^(-1)(cos(tan^(-1)x))+cos^(-1)(sin(cot^(-1)x))) ,then int_(-sqrt((pi)/(2)))^(sqrt((pi)/(2)))g(x)dx equals

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

Number ofsolution(s) ofthe equation cos^(-1)sqrt(x)-sin^(-1)sqrt(x-1)+cos^(-1)sqrt(1-x)-sin^(-1)((1)/(sqrt(x)))=(pi)/(2)

cos^(-1)sqrt(1-x)+sin^(-1)sqrt(1-x)=

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

prove that cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2))

int_(-a)^(a)(cos^(-1)x-sin^(-1)sqrt(1-x^(2)))dx is (a>0) there int_(0)^(a)cos^(-1)xdx=A) is

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
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  3. If cos^(-1)(x/2)+cos^(-1)(y/3)=theta , then 9x^2-12 x ycostheta+4y^2 i...

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  5. The value of sin^(-1)(cos(33pi)/5) is (3pi)/5 (b) -pi/(10) (c) pi/(10)...

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  6. The value of cos^(-1)("cos"(5pi)/3)+sin^(-1)("sin"(5pi)/3) is :

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  7. sin{2\ cos^(-1)(-3/5)} is equal to 6//25 (b) 24//25 (c) 4//5 (d) -24//...

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  9. If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)(...

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  10. If 4\ cos^(-1)x+sin^(-1)x=pi, then the value of x is

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  11. If tan^(-1)((x+1)/(x-1))+tan^(-1)((x-1)/x)=tan^(-1)(-7) , then the val...

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  12. If cos^(-1)x >sin^(-1)x , then 1/(sqrt(2))<xlt=1 (b) 0lt=<1/(sqrt(2)) ...

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  13. The value of sin(1/4sin^(-1)(sqrt(63))/8) is 1/(sqrt(2)) (b) 1/(sqrt(3...

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  14. Prove that cot(pi/4-2cot^(- 1)3)=7

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  15. If tan^(-1)(cottheta)=2\ theta , then theta= +-pi/3 (b) +-pi/4 (c) +-...

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  16. If sin^(-1)((2a)/(1+a^(2))) + cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((...

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  17. The value of sin(2\ (tan^(-1)0. 75)) is equal to (a) 0.75 (b) 1.5 (c) ...

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  18. If x >1 , then 2\ tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is equal to 4tan^(-...

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  19. The domain of cos^(-1)(x^2-4)i s [3,5] (b) [-1,1] [-sqrt(5),-sqrt(3)...

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  20. The value of tan(cos^(-1)3/5+tan^(-1)1/4) is (19)/8 (b) 8/(19) (c) (19...

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