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int(1-cosx)cosec^(2)x dx is equal to...

`int(1-cosx)cosec^(2)x dx` is equal to

A

`"tan" x/2+c`

B

`-"cot"x/2+c`

C

`2"tan"x/2+c`

D

`-2"cot"x/2+c`

Text Solution

Verified by Experts

The correct Answer is:
A
`int(1-cosx)cosec^(2)x dx`
`=int(1-cosx)/(1-cos^(2)x)dx=int1/(1+cosx)dx`
`=1/2 intsec^(2)x/2dx="tan"x/2+c`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 12-Paper 2 (Mathematics)
  1. Three letters, to each of which corresponds an envelope, are placed in...

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  2. The area under the curve y+sqrt(3) sin x=sin 2x between the ordinates ...

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  3. int(1-cosx)cosec^(2)x dx is equal to

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  4. The system of equations x+y+z=5, x+2y+lamdaz=mu, x+2y+3z=9 has (i)...

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  5. Find the general solution of the differential equations sec^2xtany dx...

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  6. sin[3sin^(-1)((1)/(5))] is equal to

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  7. If f:RtoR is defined by f(x)=|x|, then

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  8. The equations of the circle which pass through the origin and make int...

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  9. A circle with centre at (2, 4) is such that the line x+y+2= 0 cuts a ...

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  10. The equation of the parabola whose focus is (3,-4) and direction 6x-7y...

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  11. The equation (x^(2))/(2-lamda)-(y^(2))/(lamda-5)-1=0, represent and el...

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  12. If x^my^n = (x + y)^(m+n), then (dy/dx)(x=1, y=2) is equal to

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  13. If f'(x)=sin(log x)and y=f((2x+3)/(3-2x)), then dy/dx equals

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  14. If the mean and the variance of a binomial variable X are 2 and 1 resp...

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  15. Twelve tickets are numbered from 1 to 12. One ticket is drawn at rand...

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  16. The area enclosed between the curves y = x^(3) and y = sqrt(x) is

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  17. Write the angle between the line (x-1)/2=(y-2)/1=(z+3)/-2 and the plan...

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  18. The number of distinct values of lamda, for which the vectors -lamda^(...

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  19. The solution of the differential equation (dy)/(dx)=(x-y+3)/(2x(x-y)+5...

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  20. The general solution of equation 3 tan(theta - 15^o) = tan(theta+15^o)...

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