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A: int (1)/(3+2 cos x)dx=(2)/(sqrt(5))"T...

A: `int (1)/(3+2 cos x)dx=(2)/(sqrt(5))"Tan"^(-1)((1)/(sqrt(5))"tan" (x)/(2))+c`
R: If `a gt b` then `int (dx)/(a+b cosx)=(2)/(sqrt(a^(2)-b^(2)))Tan^(-1)[(sqrt(a-b))/(a+b)"tan"(x)/(2)]+c`

A

Both A and R are true and R is the correct explanation of A

B

Both A and R are true but R is not correct explanation of A

C

A is true but R is false

D

A is false but R is true

Text Solution

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A: int (1)/(5+4 sin x)dx=(2)/(3) Tan^(-1)((4+5tan (x//2))/(3))+c R : If a gt 0, a gt b , then int (dx)/(a+b sin x)=(2)/(sqrt(a^(2)-b^(2)))Tan^(-1)[(b+a tan (x//2))/(sqrt(a^(2)-b^(2)))]+c

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Knowledge Check

  • 2Tan^(-1)((sqrt(a-b))/(a+b)"tan"x/2)=

    A
    `Cos^(-1)((b+acosx)/(a+bcosx))`
    B
    `Cos^(-1)((b+acosx)/(a-bcosx))`
    C
    `Cos^(-1)((b-acosx)/(a+bcosx))`
    D
    `Cos^(-1)((b-acosx)/(a-bcosx))`

  • If y=(2)/(sqrt(a^(2)-b^(2)))tan^(-1) [sqrt((a-b)/(a+b))tan""(x)/(2)]

    A
    `(d^(2)y)/(dx^(2))""|_(x=(pi)/(2))=`
    B
    `(b)/(2a^(2))`
    C
    `(b)/(a^(2))`
    D
    `(2b)/(a)`

  • (d )/(dx ) { (2)/( sqrt(a ^(2) - b ^(2))) Tan ^(-1) (( sqrt (a -b ))/( a + b) tan (x )/(2 )) }=

    A
    ` a + b sin x `
    B
    `a + b cos x `
    C
    ` (1)/( a+ b sin x )`
    D
    `(1)/( a + b cos x )`

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    (d)/(dx ) { Tan ^(-1) ( sqrt(|(a -b)/(a +b)|)tan ""(x)/(2))}=

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    d/(dx) ("Tan"^(-1) (x)/(sqrt(a^2 - x^2))) =

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