Home
Class 12
MATHS
The points A(0,0),B(cosalpha,sinalpha) a...

The points `A(0,0),B(cosalpha,sinalpha)` and `C(cosbeta,sinbeta)` are the vertices of a right-angled triangle if `sin(alpha-beta)/2=1/(sqrt(2))` (b) `cos(alpha-beta)/2=-1/(sqrt(2))` `cos(alpha-beta)/2=1/(sqrt(2))` (d) `sin(alpha-beta)/2=-1/(sqrt(2))`

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(cosalpha,sinalpha) and C(cosbeta,sinbeta) are the vertices of a right-angled triangle if (a) sin((alpha-beta)/2)=1/(sqrt(2)) (b) cos((alpha-beta)/2)=-1/(sqrt(2)) (c) cos((alpha-beta)/2)=1/(sqrt(2)) (d) sin((alpha-beta)/2)=-1/(sqrt(2))

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

P(cosalpha,sinalpha), Q(cosbeta, sinbeta) , R(cosgamma, singamma) are vertices of triangle whose orthocenter is (0, 0) then the value of cos(alpha-beta) + cos(beta-gamma) + cos(gamma-alpha) is

If alpha=tan^(-1)((sqrt(3)x)/(2y-x)),beta=tan^(-1)((2x-y)/(sqrt(3y)))" then "alpha-beta=

Prove that (cos alpha+cos beta)^(2)+(sin alpha -sin beta)^(2)=4 cos^(2) ((alpha+beta)/(2))

If tanalpha=1/7,sin beta=1/(sqrt(10)), prove that alpha+2beta=pi/4

If sinalpha+sinbeta=a and cosalpha+cosbeta=b , prove that tan((alpha-beta)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2)) .

If cos alpha + cos beta = 1//2 and sin alpha+ sin beta = 1//3 , then

If tan alpha and tan beta are the roots of x^2 + ax +b =0 then (sin(alpha+beta))/(sin alpha sin beta) is equal to