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Under rotation of axes through theta , x...

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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