Question

Under rotation of axes through $\theta ,x\cos \alpha +y\sin \alpha =p$ changes to $X\cos \beta +Y\sin \beta =p$ then

• A. $\cos \beta =\cos (\alpha -\theta )$
• B. $\cos \alpha =\cos (\beta -\theta )$
• C. $\cos \beta =\sin (\alpha -\theta )$
• D. $\cos \alpha =\sin (\beta -\theta )$

Answer 1

The correct option is C $\cos \beta =\sin (\alpha -\theta )$

REF.Image

$xcos\alpha +ysin\alpha =p\to xcos\beta +ysin\beta =p$

$\therefore cos\beta =cos(\alpha -\theta )$ & $sin\beta =sin(\alpha -\theta )$