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Show that: cos(2tan^(-1)(1/7))=sin(4tan^...

Show that: `cos(2tan^(-1)(1/7))=sin(4tan^(-1)(1/3))`

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To show that \( \cos(2\tan^{-1}(1/7)) = \sin(4\tan^{-1}(1/3)) \), we will evaluate both sides step by step. ### Step 1: Evaluate the Left-Hand Side (LHS) We start with the LHS: \[ \text{LHS} = \cos(2\tan^{-1}(1/7)) ...
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Prove that: tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=pi/4

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluate: tan(2tan^(-1)(1/5))

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  2. Prove that sin^-1[3/5]+sin^-1[4/5]=pi/2

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

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  4. Find the value of expression: sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2)...

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  5. Find the principal value of the following: """"" sin^(-1){cos(sin^(...

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  6. If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/...

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  7. Find the domain of the function f(x)=sin^(-1)sqrt(x-1)

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  8. Find the domain of f(x)=sin^(-1)x+cosxdot

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  9. Find the domain of f(x)=sin^(-1)(-x^2)dot

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  10. Find the domain of the function f(x)=sin^(-1)(2x-3)

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  11. Find the value of sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}]

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  12. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/2, find the value of x^2+y^2+z...

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  13. Find the domain of function: f(x)=sin^(-1)sqrt(x^2-1)

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  14. Prove that: 2tan^(-1) {1/2}+tan^(-1) {1/7}=tan^(-1) {(31)/(17)}

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  15. Solve the equation: cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)...

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  16. If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, prove that x^2+y^2+z^2+2x y z=1.

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  17. If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(...

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  18. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

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  19. Solve the following equations: sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^...

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  20. Prove that sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))

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