Home
Class 11
MATHS
Given that (1+sqrt(1+x))tany=1+sqrt(1-x)...

Given that `(1+sqrt(1+x))tany=1+sqrt(1-x)` . Then `sin4y` is equal to
(a)`4x`
(b) `2x`
(c) `x`
(d) none of these

Text Solution

Verified by Experts

Let` x=costheta`
`1+x=1+costheta`
`=2cos^2(theta/2)`
`sqrt(1+x)=sqrt2cos(theta/2)`
`1-x=1-costheta`
`=2sin^2(theta/2)`
`sqrt(1-x)=sqrt2si(theta/2)`
`tany=(1+sqrt(1-x))/(1+sqrt(1+x))`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b) 2x (c) 2/x (d) none of these

Ifint_(log2)^x(dy)/(sqrt(e^y-1))=pi/6,"then " x " is equal to" (a)4 (b) 1n 8 (c) 1n 4 (d) none of these

The degree of the differential equation satisfying sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) is (a) 1 (b) 2 (c) 3 (d) none of these

If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) is equal to- (a) log"(sqrt(2)+1) (b) 1 (c) 1+sqrt(2) (d) none of these

int(sin^(-1)x)/(sqrt(1-x^(2)))dx is equal to

If x in (pi,(3pi)/2), then 4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x) is always equal to (a) 1 (b) 2 (c) -2 (d) none of these

Ifint_(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto" 4 (b) 1n 8 (c) 1n 4 (d) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

lim_(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (b) 0 (c) 2 (d) none of these

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. If theta is eliminated from the equations x=a"cos"(theta-alpha) and y=...

    Text Solution

    |

  2. If tanx=b/a , then sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b)) is equal to (...

    Text Solution

    |

  3. Given that (1+sqrt(1+x))tany=1+sqrt(1-x) . Then sin4y is equal to (a...

    Text Solution

    |

  4. If cos2B=(cos(A+C))/("cos"(A-C)), then tanA ,t a n B ,tanC are in (a...

    Text Solution

    |

  5. If ("cos"(x-y))/("cos"(x+y))+("cos"(z+t))/(cos(z-t))=0 , then the val...

    Text Solution

    |

  6. For all theta in [0,pi/2] show that cos(sintheta)gtsin(costheta)

    Text Solution

    |

  7. Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma...

    Text Solution

    |

  8. The maximum value of y=1/(sin^6x+cos^6x) is

    Text Solution

    |

  9. The value of cos e c10^0+cos e c50^0-cos e c70^0 is

    Text Solution

    |

  10. Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e...

    Text Solution

    |

  11. Given that f(ntheta)=(2sin2theta)/(cos2theta-cos4ntheta), and f(theta)...

    Text Solution

    |

  12. If sin^2(theta-alpha)c a salpha=cos^2(theta-alpha)sinalpha=msinalphaco...

    Text Solution

    |

  13. The maximum value of 4sin^2x+3cos^2x+sin(x/2)+cos(x/2) is

    Text Solution

    |

  14. Find the range of f(x)=1/((cosx-3)^2+(sinx+4)^2)

    Text Solution

    |

  15. Find the maximum value of sqrt(3)sinx+cosx and x for which a maximum ...

    Text Solution

    |

  16. In triangle A B C , if /A=pi/4, then find all possible values of tanBt...

    Text Solution

    |

  17. If A=pi/5, then find the value of sum(r=1)^8tan(r A)*tan((r+1)A)dot

    Text Solution

    |

  18. Prove that (1+tan1^0)(1+tan2^0)......(1+tan45^0)=2^(23)dot

    Text Solution

    |

  19. Find the value of (cot25^0+cot55^0)/(tan25^0+tan55^0)+(cot55^0+cot100...

    Text Solution

    |

  20. If tanx+tan2x+tan3x=tanxtan2xtan3x then value of |sin3x+cos3x| is

    Text Solution

    |