Home
Class 12
MATHS
The value of sin^3 10^0+sin^3 50^0-sin^3...

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

A

`-(3)/(2)`

B

`(3)/(4)`

C

`-(3)/(4)`

D

`-(3)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have `sin^(3)10^(@)+sin^(3)50^(@)-sin^(3)70^(@)`
`=(1)/(4)[(3sin10^(@)-sin30^(@))+(3sin50^(@)-sin150^(@))-(3sin70^(@)-sin210^(@))]`
`=(1)/(4)[3(sin10^(@)+sin50^(@)-sin70^(@))-(3)/(2)]`
`=(1)/(4)[3(sin 10^(@)-2cos60^(@).sin10^(@))-(3)/(2)]=-(3)/(8)`
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 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

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

The value of sin 50^(0)-sin 70^0+sin 10^0 is equal to a. 0 b. 1 c. 2 d. 1//2

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

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^@

The value of (cos^3 20^@-cos^3 70^@)/(sin^3 70^@-sin^3 20^@) is (a) 1/2 (b) 1/(sqrt(2)) (c) 1 (d) 2

3/(10) is equal to (a)3.1 (b) 1.3 (c) 0.3 (d) 0.03

The value of sin^2 75^0-sin^2 15^0 is a. 1//2 b. sqrt(3)//2 c. 1 d. 0

Prove that: \ sin 10^0sin 50^0sin 60^0sin 70^0=(sqrt(3))/(16)

Evaluate: sin(3\ sin^(-1)0. 4)

CENGAGE ENGLISH-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. If 2 sin 2alpha= | tan beta+ cot beta |alpha,beta, in((pi)/(2),pi), th...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. cot16^0cot44^0+cot44^0cot76^0-cot76^0cot16^0= 1 (b) 2 (c) 3 (d) ...

    Text Solution

    |

  17. If tanx=b/a , then sqrt((a+b)/(a-b))+sqrt((1-b)/(a+b)) is equal to 2s ...

    Text Solution

    |

  18. Given that (1+sqrt(1+x))tany=1+sqrt(1-x) . Then sin4y is equal to 4x ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |