Home
Class 12
MATHS
Let PQR be a triangle of area Delta with...

Let PQR be a triangle of area `Delta` with `a=2,b=7/2 and c=5/2`, where a,b and c are the lengths of the sides of the triangle opposite to the angles at P,Q and R respectively. Then `((2sinP-sin2P)/ (2sinP+sin2P))` equals

A

`(3)/(4Delta)`

B

`(45)/(4Delta)`

C

`((3)/(4Delta))^(2)`

D

`((45)/(4Delta))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C

`(2 sin P - 2 sin P cos P)/(2 sin P + 2 sin P cos P)`
`= (1- cos P)/(1 +cos P) = (2"sin"^(2) (P)/(2))/(2 "cos"^(2) (P)/(2)) = "tan"^(2) (P)/(2)`
`= ((s-b) (s-c))/(s(s-a))`
`= (((s-b) (s-c))^(2))/(Delta^(2)) = ((((1)/(2)) ((3)/(2)))^(2))/(Delta^(2)) = ((3)/(4Delta))^(2)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Multiple correct Answer Type)|4 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Matrix Match Type)|1 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Single correct Answer type)|2 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1119 Videos

Similar Questions

Explore conceptually related problems

Let p,q,r be the sides opposite to the angles P,Q, R respectively in a triangle PQR if 2prsin((P-Q+R)/(2)) equals

Let p,q,r be the sides opposite to the angles P,Q,R respectively in a triangle PQR. Then 2prsin((P-Q+R)/2) equal

In a DeltaABC, a,b,c are the sides of the triangle opposite to the angles A,B,C respectively. Then the value of a^3sin(B-C)+b^3 sin(C-A)+c^3 sin(A-B) is equal to

Let p,q,r be the sides opposite to the angles P,Q, R respectively in a triangle PQR if r^(2)sin P sin Q= pq , then the triangle is

Using vectors , prove that in a triangle ABC a/(sin A) = b/(sin B) = c/(sin C) where a,b,c are lengths of the ideas opposite to the angles A,B,C of triangle ABC respectively .

In a triangle DeltaXYZ, let a, b, and c be the length of the sides opposites to the angles X,Y and Z, respectively.If 1+cos2X-2cos2Y=2sinXsinY , then possible value(s) of a/b is (are)

Using vectors , prove that in a triangle ABC a^(2)= b^(2) + c^(2) - 2bc cos A where a,b,c are lengths of the ideas opposite to the angles A,B,C of triangle ABC respectively .

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

In a triangle DeltaXYZ , let a,b and c be the lengths of the sides opposite to the angles X,Y and Z, respectively. If 2(a^2-b^2)=c^2 and lambda=sin(X-Y)/(sinZ, then possible values of n for which cos(npilambda)=0 is (are)