Home
Class 12
MATHS
The value of expression (2sin^2 91^0-1)(...

The value of expression `(2sin^2 91^0-1)(2sin^2 92^0-1)......(2sin^2 180^0-1)` is equal to

A

0

B

1

C

`2^90`

D

`2^90-90`

Text Solution

Verified by Experts

The correct Answer is:
A
`(2sin^2 91^@-1)(2sin^2 92^@-1)...(2sin^2 180^@-1)`,
In this product there exists a factor `(2sin^2 135^@-1)`, which is equal to zero
Thus, the product of all terms is zero.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.14|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

The value of the expression (tan^2 20^0-sin^2 20^0)/(tan^2 20^0+sin^2 20^0) is__________

The value of the expression (tan^2 20^0-sin^2 20^0)/((tan^2 20^0)(sin^2 20^0)) is__________

cos^(-1)(1/2)+2sin^(-1)(1/2) is equal to

The value of sin^2 12^0+sin^2 21^0+sin^2 39^0+sin^2 48^0-sin^2 9^0-sin^2 18^0 is _______

If x^2!=n pi-1, n in N . Then, the value of int x sqrt((2sin(x^2+1)-sin2(x^2+1))/(2sin(x^2+1)+sin2(x^2+1)))dx is equal to:

sin(2sin^(-1) 0.8)=

(2sin^(2)x -1) +1=0

The value of expression (2(sin1^0+sin2^0+sin3^0+...+sin89^0))/(2(cos1^0+cos2^0++cos44^0)+1) (a) sqrt(2) (b) 1/(sqrt(2)) (c) 1/2 (d) 0

The value of the expression 1-sin^2y/(1+cosy)+(1+cosy)/siny-siny/(1-cosy) is equal to

Show that sin^2 5^0+sin^2 10^0+sin^2 15^0+....+sin^2 90^0=9 1/2dot

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. Prove that, SinA/(1-cosA) =CosecA+cotA

    Text Solution

    |

  2. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

    Text Solution

    |

  3. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)......(2sin^2 18...

    Text Solution

    |

  4. If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right an...

    Text Solution

    |

  5. If sintheta+costheta=1/5and 0lethetaltpi" then "cottheta is

    Text Solution

    |

  6. If π<α<(3π)/2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/...

    Text Solution

    |

  7. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

    Text Solution

    |

  8. The least value of 3sin^2theta+4cos^2theta is

    Text Solution

    |

  9. The minimum value of sin^4theta+cos^4theta is

    Text Solution

    |

  10. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

    Text Solution

    |

  11. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

    Text Solution

    |

  12. Range of f(theta)=cos^2theta(cos^2theta+1)+3sin^2theta is

    Text Solution

    |

  13. If 0<theta<pi, then minimum value of 3sintheta+cos e c^3theta is 4 (b)...

    Text Solution

    |

  14. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

    Text Solution

    |

  15. The set of values of lambda in R such that sin^2theta+costheta=lambda...

    Text Solution

    |

  16. Let A=sin^6theta+cos^8theta, " then "A("max") is

    Text Solution

    |

  17. Minimum value of y=25sin^2x+36cos e c^2xAAx in R is

    Text Solution

    |

  18. If aa n db are positive quantities such that a > b , the minimum value...

    Text Solution

    |

  19. If y=(cosx+secx)^2+(tanx+cotx)^2 then the minimum value of y,AAx in R,...

    Text Solution

    |

  20. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |