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If a1,a2,a3 ,….""an is an aritmetic p...

If `a_1,a_2,a_3 ,….""a_n` is an aritmetic progression with common difference d. prove that
` tan [ tan ^(-1) ((d)/( 1+ a_1a_2))+ tan^(-1) ((d)/(1+a_2a_3))+…+((d)/(1+a_n a_( n-1))) ] = (a_n -a_1)/(1 +a_1 a_n )`

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FULL MARKS-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE -4.6
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  3. If sin^(-1)x+sin^(-1)y=(2pi)/(3)",then"cos^(-1)x+cos^(-1)y is equal to

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  4. sin^(-1)""(3)/(5)-cos^(-1)""(12)/(13)+sec^(-1)""(5)/(3)-cosec^(-1)(13)...

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  5. If sin^(-1)x=2sin^(-1)alpha has a solution, then

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  6. sin^(-1)(cosx)=(pi)/(2)-x is valid for

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  7. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) , the value of x^(2017)+y^(...

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  8. If cot^(-1) x = (2pi)/7 for some x in R the value of tan^(-1) x is...

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  9. The domain of the function defined by f(x)=sin^(-1)sqrt(x-1) is

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  10. If x=(1)/(5),"the value of"cos(cos^(-1)x+2sin^(-1)x) is

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  11. tan^(-1)((1)/(4))+tan^(-1)((2)/(9)) is equal to

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  12. If the function f(x)=sin^(-1)(x^(2)-3)" then "x belongs to

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  13. If cot^(-1)2andcot^(-1)3 are two anges of a triangle, then the third a...

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  14. sin^(-1)[tan""(pi)/(4)]-sin^(-1)[sqrt((3)/(x))]=(pi)/(6). Then x is a ...

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  15. sin^(-1)(2cos^(2)x-1)+cos^(-1)(1-2sin^(2)x)=

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  16. If cot^(-1)(sqrt(sinalpha))+tan^(-1)(sqrt(sinalpha))=u,"then"cos2u"is ...

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  17. sin^(-1) ((2x)/(1 + x^(2)))

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  18. The equation tan^(-1)x-cot^(-1)x=tan^(-1)((1)/(sqrt(3))) has

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  19. If cos^(-1)x + cot^(-1) (1/2) = pi/2 then x is equal to

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  20. If sin^(-1)""(x)/(5)+cosec^(-1)""(5)/(4)=(pi)/(2), then the value of x...

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  21. sin(tan^(-1)x)absxlt1 is equal to

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