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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 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)`
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