If a cos 0 + b sin 0 = p, a sin 0- b cos 0 = q then
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Answer:
Given : acosθ+bsinθ=m ---( 1 )
asinθ−bcosθ=n ---( 2 )
Squaring (1) and (2), we get
a
2
cos
2
θ+b
2
sin
2
θ+2absinθcosθ=m
2
---(3)
and
a
2
sin
2
θ+b
2
cos
2
θ−2absinθcosθ=n
2
---(4)
Adding (3) and (4)
a
2
(sin
2
θ+cos
2
θ)+b
2
(sin
2
θ+cos
2
θ)=m
2
+n
2
or
a
2
+b
2
=m
2
+n
2
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