Home
Class 12
MATHS
If t a n^2theta=2t a n^2varphi+1 , prove...

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

A

`-1`

B

0

C

1

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
`tan^(2)theta=2tan^(2)phi+1`
or `1+tan^(2)theta=2(1+tan^(2)phi)`
`rArr sec^(2)theta=2sec^(2)phi`
`rArr cos^(2)phi=2cos^(2)phi=1=+cos2theta`
`rArr cos 2theta=cos^(2)phi-1=-sin^(2)phi`
`rArr sin^(2)phi+cos2theta=0`
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

If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

Prove that 1-cos^(2)theta-sin^(2)theta=0

If t a n^2theta=1-a^2 , prove that sectheta+t a n^3thetacos e ctheta=(2-a^2)^(3//2).

If tantheta=1/2a n dt a nvarphi=1/3, then the value of theta+varphi is pi/6 (b) pi (c) 0 (d) pi/4

varphi ^2=0 represents

If sin2theta+sin2varphi=1/2a n d\ cos2theta+cos2varphi=3/2 , then cos^2(theta-varphi)= a. 3//8 b. 5//8 c. 3//4 d. 5//4

If tan alpha = (sin theta sin varphi)/(cos theta + cos varphi) , prove that one of the values of tan\ alpha/2 is tan\ theta/2 tan\ varphi/2 .

If theta = (pi)/(2 ^(n) +1) prove that 2 ^(n) cos theta cos 2 theta cos 2 ^(2) theta…. Cos 2 ^(n -1) theta =1

If m tan(alpha-theta)/( cos^2 theta) = n (tan theta)/ (cos^2 (alpha - theta) the prove that 2 theta = alpha - [ tan^(-1) ((n-m)/(n+m)) tan alpha]

If sin theta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/(1-n)tanalpha .

CENGAGE ENGLISH-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. If cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |