Home
Class 12
MATHS
दर्शाइए कि (i) sin^(-1)(2xsqrt(1-x^(2)...

दर्शाइए कि
(i) `sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1),-(1)/(sqrt(2)) le x le (1)/(sqrt(2))`
(ii) `sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1) x,(1)/(sqrt(2)) le x le 1`

Text Solution

Verified by Experts

Put `x=sintheta`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4D|6 Videos
  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Objective Questons|57 Videos
  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4B|22 Videos
  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos
  • LINEAR DIFFERENTIAL EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|27 Videos

Similar Questions

Explore conceptually related problems

Show that (i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

Prove that sin^(-1) (2xsqrt(1-x^2))=2cos^(-1)x,1/sqrt2 le x le 1

Prove that : sin^(-1) (2x sqrt(1-x^(2)))= 2 sin^(-1) x, - 1/(sqrt(2)) le x le 1/(sqrt(2))

Prove that : sin^(-1) (2x sqrt(1-x^(2)) ) = 2 sin^(-1) x , -1/(sqrt(2))le x le 1/(sqrt(2)

y = sin ^(-1)(2xsqrt(1 - x^(2))),-(1)/sqrt(2) lt x lt (1)/sqrt(2)

If -1 le x le -(1)/sqrt(2) then sin^(-1)2xsqrt(1-x^(2)) equals

sin^(-1)(xsqrt(x)),0 le x le 1

If -1le x le -(1)/(sqrt(2)) , then prove that sin^(-1)(2xsqrt(1-x^2))=-2pi+2cos^(-1)x .

int(1)/(cos^(-1)x.sqrt(1-x^(2)))dx=

If 1/sqrt(2) le x le 1 and sin^(-1)(2xsqrt(1-x^(2))) = A + B sin^(-1)x , then (A,B)=