Home
Class 12
MATHS
If x in (pi,(3pi)/2),t h e n4cos^2(pi/4-...

If `x in (pi,(3pi)/2),t h e n4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x)` is always equal to 1 (b) 2 (c) `-2` (d) none of these

A

1

B

2

C

`-2`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
`4cos^(2)((pi)/(4)-(x)/(2))+sqrt(4sin^(4)x+sin^(2)2x)`
`=4cos^(2)((pi)/(4)-(x)/(2))+sqrt(4sin^(2)x(cos^(2)x+sin^(2)x))`
`=2(1+cos((pi)/(2)-x))+2|sinx|`
`=2+2sinx-2sinx` [as `x in(pi,(3pi)/(2)`)]
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

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

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If x in (pi,(3pi)/2), then 4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x) is always equal to (a) 1 (b) 2 (c) -2 (d) none of these

The total number of solution of cosx=sqrt(1-sin2x) in [0,2pi] is equal to 2 (b) 3 (c) 5 (d) none of these

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these

tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b) 2x (c) 2/x (d) none of these

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)=-(3pi^2)/4, then lim_(x->-pi)(f(x))/("sin"(sinx) is equal to (a) 0 (b) pi (c) 2pi (d) none of these

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi,t h e nx^4+y^2+z^4+4x^2y^2z^2=K(x^2y^2+y^2z^2+z^2x^2), where K is equal to 1 (b) 2 (c) 4 (d) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

Prove that cos ((3pi)/(4)+x)-cos ((3pi)/(4)-x)=-sqrt2 sin x

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If sinx+cosx=(sqrt(7))/2, where x in 1s t quadrant, then tanx/2 is equ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. If tan beta=2sin alpha sin gamma co sec(alpha+gamma), then cot alpha,c...

    Text Solution

    |

  11. the value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to

    Text Solution

    |

  12. If cos^3xsin2x=sum(r=0)^n axsin(r x),AAx in R then

    Text Solution

    |

  13. cos^6pi/9-33tan^4pi/9+27tan^2pi/9 is equal to 0 (b) sqrt(3) (c) 3 ...

    Text Solution

    |

  14. Given that a , b , c , are the side of a A B C which is right angled ...

    Text Solution

    |

  15. If theta=3alphaa n dsintheta=a/(sqrt(a^2+b^2)), the value of the expre...

    Text Solution

    |

  16. tan 6^@ . Tan 42^@. Tan 66^@ . Tan 78^@ is

    Text Solution

    |

  17. In triangle A B C , if angle c is 90 and the area of triangle is 30 s...

    Text Solution

    |

  18. If sqrt(2)cos A=cos B+cos^3B ,a n dsqrt(2)sinA=sinB-sin^3Bt h e nsin(A...

    Text Solution

    |

  19. In a right angled triangle the hypotenuse is 2sqrt(2) times the perpen...

    Text Solution

    |

  20. A circular ring of radius 3cm hangs horizontally form a point 4cm v...

    Text Solution

    |