Home
Class 12
MATHS
If the line x=y=z intersect the line sin...

If the line `x=y=z` intersect the line `sin Adotx+sin Bdoty+sin Cdotz=2d^2,sin2Adotx+sin2Bdoty+sin2Cdotz=d^2,` then find the value of `sinA/2dotsinB/2dotsinC/2w h e r eA ,B ,C` are the angles of a triangle.

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \(\sin \frac{A}{2} \cdot \sin \frac{B}{2} \cdot \sin \frac{C}{2}\) where \(A\), \(B\), and \(C\) are the angles of a triangle. The lines given are \(x = y = z\) and two equations involving sine functions. ### Step-by-Step Solution: 1. **Parameterize the Line**: Since \(x = y = z\), we can let \(x = y = z = \lambda\). 2. **Substitute into the First Equation**: ...
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

  • TRIGONOMETRIC EQUATIONS

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

Similar Questions

Explore conceptually related problems

If 2sin^(2)A=sin^(2)60^(@)+sin^(2)45^(@) , then find the value of sin A.

If the line x=y=z intersect the lines xsinA+ysinB+zsinC-2d^(2)=0=xsin(2A)+ysin(2B)+zsin(2C)-d^(2), where A, B, C are the internal angles of a triangle and "sin"(A)/(2)"sin"(B)/(2)"sin"(C)/(2)=k then the value of 64k is equal to

If sin^-1x+sin^-1y+sin^-1z=(3pi)/2 , then find the value of x^2+y^2+z^2

In a triangle ABC sin (A/2) sin (B/2) sin (C/2) = 1/8 prove that the triangle is equilateral

In a triange ABC, if sin(A/2) sin (B/2) sin(C/2) = 1/8 prove that the triangle is equilateral.

If sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2 , then find the value of x^2+y^2+z^2

If sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2 , then find the value of x^2+y^2+z^2

If r=sqrt(8/3) and R=35/(4sqrt6) then the value of sin X/2 sin Y/2 sin Z/2 =

If the incircle of the triangle ABC passes through its circumcenter, then find the value of 4 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2)

If in triangle A B C ,/_C=45^0 then find the range of the values of sin^2A+sin^2Bdot