Home
Class 12
MATHS
Find the value of (cos^2pi/16+ cos^2 (3p...

Find the value of `(cos^2pi/16+ cos^2 (3pi)/16+cos^2(5pi)/16+cos^2(7pi)/16)`.

Text Solution

Verified by Experts

`L.H.S.=cos^2. pi/16+cos^2.(3pi)/16+cos^2(pi/2-(3pi)/16)`
`+cos^2(pi/2-pi/16)`
`=cos^2.pi/16+cos^2.(3pi)/16+sin^2.(3pi)/16+sin^2.pi/16`
`=(cos^2. pi/16+sin^2. pi/16)+(cos^2(3pi)/16+sin^2(3pi)/16)`
`=1+1=2`
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

Find the value of sin^2(pi/16)+ sin^2 ((3pi)/16)+sin^2 ((5pi)/16)+sin^2((7pi)/16) .

Evaluate : cos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)

Find the value of 16cos(pi/15).cos((2pi)/15).cos((4pi)/15).cos((8pi)/15)

Find the value of 2cos^3(pi/7)-cos^2(pi/7)-cos(pi/7)

cos(pi/14) + cos ((3pi)/14) + cos((5pi)/14) =

Find the value of (1+cos (pi/8))(1+cos(3pi/8))(1+cos(5pi/8))(1+cos(7pi/8))

Prove that cos^2( pi/8)+cos^2((3pi)/8)+cos^2 ((5pi)/8)+cos^2 ((7pi)/8)=2.

Find the value and tan (pi/16) tan ((3pi)/16) tan((5pi)/16)tan((7pi)/16) .

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Find the value of (cos^2pi/16+ cos^2 (3pi)/16+cos^2(5pi)/16+cos^2(7pi)...

    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

    |