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 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 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

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 sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to 1 (b) 2 (c) 1/2 (d) none of these

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to 1 (b) 2 (c) 1/2 (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"

cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1))) is equal to sqrt(2)-1 (b) pi/4 (c) (3pi)/4 (d) non eoft h e s e

If n=2m+1,m in N uu {0}, then int_0^(pi/2)(sin nx)/(sin x) dx is equal to (i) pi (ii) pi/2 (iii) pi/4 (iv) none of these

If sin^(-1)x-cos^(-1)x=pi/6 , then x= (a) 1/2 (b) (sqrt(3))/2 (c) -1/2 (d) none of these

int _(-pi)^(pi) (sin^(4)x)/(sin^(2) x + cos^(4) x )dx is equal to

2sin^2x+sin^2(2x)=2 , -piltxltpi then x equals (A) +- pi/2 (B) +- pi/4 (C) +-(3pi)/4 (D) none of these

CENGAGE ENGLISH-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single Correct Answer Type)
  1. If sinx+cosx=sqrt7/2 where xin[0,pi/4] then tan(x/2) is equal to

    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)xxcot(y...

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

    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=3alpha and sin theta=(a)/(sqrt(a^(2)+b^(2)) , the value of th...

    Text Solution

    |

  16. tan 6 ^(@) tan 42 ^(@) tan 66 ^(@) tan 78^(@) =1

    Text Solution

    |

  17. In triangle A B C , if angle is 90^0 and the area of triangle is 30 sq...

    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 3 cm hangs horizontally from a point 4 cm ve...

    Text Solution

    |