Home
Class 12
MATHS
If the points A(0,0),B(cosalpha,sinalpha...

If the points `A(0,0),B(cosalpha,sinalpha)`, and `C(cosbeta,sinbeta)` are the vertices of a right- angled triangle, then

A

`sin.(alpha-beta)/(2)=(1)/(sqrt2)`

B

`cos.(alpha-beta)/(2)=(1)/(sqrt2)`

C

`cos.(alpha-beta)/(2)=-(1)/(sqrt2)`

D

`sin.(alpha-beta)/(2)=-(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Since `AB=AC=1`, the triangle is right -angled at point A. we have `tanalphatanbeta=-1` or `cos(alpha-beta)=0or alpha-beta=+-(pi)/(2)`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Comprehension)|10 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Single)|59 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The points A(0, 0), B(cos alpha, sin alpha) and C(cos beta, sin beta) are the vertices of a right angled triangle if :

Show that the points A(-5, 6), B(3, 0) and C(9, 8) are the vertices of an isosceles right-angled triangle. Calculate its area.

Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle.

Show that the points A(2,-1,3),B(1,-3,1) and C(0,1,2) are the vertices of an isosceles right angled triangle.

The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p.

The points A(4,7),B(p,3) and C(7,3) are the vertices of a right triangle,right-angled at B , Find the values of P.

Without using Pythagoras theorem,show that the points A(0,4),B(1,2) and C(3,3) are the vertices of a right angled triangle.

Without using pythagoras theorem, show that the points A(-1,3) ,B(0,5) and C(3,1) are the vertices of a right angled triangle

Using vector method, show that the points A(1,-1,0), B(4,-3,1) and C(2,-4,5) are the vertices of a right -angled triangle.