Question

lf $(\cos \alpha ,\cos \beta )$ are the new co-ordinates of a point $P$ when the axes are translated to the point $(1,1)$ then the original co-ordinates are

• A. $(2{\cos }^2\frac{\alpha }{2},2{\cos }^2\frac{\beta }{2})$
• B. $(2{\cos }^2\frac{\alpha }{2},2{\sin }^2\frac{\beta }{2})$
• C. $(2{\sin }^2\frac{\alpha }{2},2{\cos }^2\frac{\beta }{2})$
• D. $(-2{\cos }^2\frac{\alpha }{2},-2{\cos }^2\frac{\beta }{2})$

Answer 1

Answer: (A)

$(2{\cos }^2\frac{\alpha }{2},2{\cos }^2\frac{\beta }{2})$

Let original co-ordinates be $(h,k)$

Then $(h,k)=(1+\cos \alpha ,1+\cos \beta )$

$=(2{\cos }^2\frac{\alpha }{2},2{\cos }^2\frac{\beta }{2})$