Home
Class 12
MATHS
The value of cos^2 10^0-cos10^0cos50^0+c...

The value of `cos^2 10^0-cos10^0cos50^0+cos^2 50^0` is equal to `4/3` (b) `1/3` (c) `3/4` (d) `3`

A

`(4)/(3)`

B

`(1)/(3)`

C

`(3)/(4)`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
C
`cos^(2)10^(@)-cos10^(@)cos50^(@)+cos^(2)50^(@)`
`=(1)/(2)[1+cos 20^(@)-(cos60^(@)+cos40^(@))`
`+(1+cos 100^(@))]`
`=(1)/(2)[1+cos20^(@)-(1)/(2)-cos40^(@)+1-cos80^(@)]`
`=(1)/(2)[(3)/(2)+cos 20^(@)-(2cos 60^(@)cos20^(@))]=(3)/(4)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Exercise (Multiple Correct Answer Type)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Exercise (Linked Comprehension Type)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Concept App. 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

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

Write the value of cos1^0+cos2^0+cos3^0++cos 180^0dot

The values of cos^2 73^0+cos^2 47^0-sin^2 43^0+sin^2 107^0 is equal to: (b) 1/2 (c) (sqrt(3))/2 (d) sin^2 73^@+cos^4 73^@

Prove that: cos 10^0cos30^0cos 50^0cos 70^0=3/(16)

Prove that: cos 10^0cos30^0cos 50^0cos 70^0=3/(16)

The value of sin^3 10^0+sin^3 50^0-sin^3 70^0 is equal to (a) -3/2 (b) 3/4 (c) -3/4 (d) -3/8

Prove that: sin 80^0-cos 70^0=cos 50^0

find the value of sin60^@cos3 0^@+sin3 0^@cos6 0^@

The value of cos 52^0+cos 68^0+cos 172^0 is a. 0 b. 1 c. 2 d. 3//2

The value of cos^(2)10^(@)-cos10^(@)cos 50^(@)+cos^(2)50^(@) is k/2 . The value of k is ________.

CENGAGE ENGLISH-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. (sin^2A-sin^2B)/(sinAcosA-sinBcosB) is equal to (a) tan(A-B) (b...

    Text Solution

    |

  2. If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2...

    Text Solution

    |

  3. The value of cos^2 10^0-cos10^0cos50^0+cos^2 50^0 is equal to 4/3 (b)...

    Text Solution

    |

  4. If t a n^2theta=2t a n^2varphi+1 , prove that cos2theta+s in^2varphi=0...

    Text Solution

    |

  5. If sinx+cos e cx+tany+coty=4 where xa n dy in [0,pi/2],t h e ntany/2 i...

    Text Solution

    |

  6. If 2 sin 2alpha= | tan beta+ cot beta |alpha,beta, in((pi)/(2),pi), th...

    Text Solution

    |

  7. If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the va...

    Text Solution

    |

  8. The value of sin^3 10^0+sin^3 50^0-sin^3 70^0 is equal to -3/2 (b) 3/...

    Text Solution

    |

  9. Let P(x)=((1-cos2x+sin2x)/(1+cos2x+s in2x))^2+((1+cotx+cot^2x)/(1+tanx...

    Text Solution

    |

  10. If (3-tan^(2)""(pi)/(7))/(1-tan^(2)""(pi)/(7))=kcos""(pi)/(7) then the...

    Text Solution

    |

  11. cos e c(360^0)/7+cos e c(540^0)/7= cos e c(180^0)/7 (b) cos e c(90^0...

    Text Solution

    |

  12. If theta1a n dtheta2 are two values lying in [2,2pi] for which t a nth...

    Text Solution

    |

  13. If tantheta=sqrt(n), where n in N ,geq2,t h e nsec2theta is always a ...

    Text Solution

    |

  14. If sin2theta=cos3thetaa n dtheta is an acute angle, then sintheta equa...

    Text Solution

    |

  15. If cosx= tany, cosy= tanz and cosz= tanx, prove that sinx= siny= sinz ...

    Text Solution

    |

  16. The value of 70^0+4cos70^0 is 1/(sqrt(3)) (b) sqrt(3) (c) 2sqrt(3) ...

    Text Solution

    |

  17. If sinx+cosx=sqrt7/2 where xin[0,pi/4] then tan(x/2) is equal to

    Text Solution

    |

  18. If (tan3A)/(tanA)=k(k!=1) then which of the following is not true? (co...

    Text Solution

    |

  19. If x in (pi,(3pi)/2),t h e n4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x) is...

    Text Solution

    |

  20. If cosx=(2cosy-1)/(2-cosy), where x , y in (0,pi) then tan(x/2)xxcot(y...

    Text Solution

    |