Under rotation of axes through `theta` , `x cosalpha + ysinalpha=P` changes to `Xcos beta + Y sin beta=P` then .
(a) `cos beta = cos (alpha - theta)`
(b) `cos alpha= cos( beta - theta)`
(c) `sin beta = sin (alpha - theta)`
(d) `sin alpha = sin ( beta - theta)`
A
`cos beta = cos (alpha - theta)`
B
`cos alpha = cos (beta - theta)`
C
`sin beta = sin (alpha - theta)`
D
`sin alpha = sin (beta - theta)`
Text Solution
Verified by Experts
The correct Answer is:
A, C
`x cos alpha +y sin alpha +P` Axis rotated through angle `theta`. Transformed equation `cos alpha (x cos theta - y sin theta) +sin alpha (x sin theta +y cos theta) = P` `x cos (alpha -theta) +y sin (alpha -theta) = P rArr x cos beta +y sin beta = P` where, `cos beta = cos (alpha-theta), sin beta = sin (alpha - theta)`
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