Home
Class 12
MATHS
For acute angle theta, Prove that sinthe...

For acute angle `theta`, Prove that `sinthetaltthetalttantheta`.

Text Solution

Verified by Experts

Consider the circle with unit radius as show in the following figure.
From the figure, from position of C on the circle
Area of `DeltaOBClt" Area of sector " Delta OBD`
`:. 1/2(CE)(OB)lt1/2thetalt1/2(OB)(BD)`
`rArr1/2(sintheta)(1)lt1/2thetalt1/2(1)(tantheta)`
`rArr sinthetaltthetalttantheta`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise example|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.1|8 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

For acute angle theta , prove the following: sec^2theta+cosec^2thetage4

For which value of an acute angle theta ,(i) ( cos theta )/( 1-sin theta ) +(cos theta )/( 1+sin theta ) =4 is true ? For which value of 0^(@) le theta le 90 ^(@) , above equation is not defined?

If theta is a positive acute angle and tan theta=3/4, find sin theta and sec theta

If a unit vector veca makes angles (pi)/(3) with hati,(pi)/(4) with hatj and an acute angle theta with hatk then find theta and hence , the components of veca .

For any two positive acute angles theta and phi if sin(theta+phi)=k sin(theta-phi) and 33(cos2phi-cos2theta)+cos2thetacos2phi=1

Prove that, cot theta - tan theta = 2cot 2 theta

Angle of dip at a place = theta , if the angle of dip in a vertical plane making angle delta with the magnetic meridian be theta' , show that , tantheta':tan theta=secdelta:1

If theta positive acute angle and tan theta+sectheta=2/sqrt(3) find sin theta

If alpha, beta, gamma are positive acute angles, prove that sin alpha+sin beta+ sin gamma gt sin (alpha+ beta+ gamma)

If theta and (2theta - 45^@) are acute angles such that cosec theta cos(2theta - 45^@) = 1 then tan theta equals____

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. For acute angle theta, Prove that sinthetaltthetalttantheta.

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  6. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  7. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b, then, (b^2-1)^2(a^2+4...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is (a) -15 (b) ...

    Text Solution

    |

  12. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  13. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  14. Find the cartesian co-ordinates of the points whose polar co-ordinates...

    Text Solution

    |

  15. Simplify :cos(x-(pi)/(2)).tan((3pi)/(2)+x)

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |