72. If a sin a + b cos 0 =p and
a cos 0 + b sino =q, then
(ap – bq)2+ (aq – bp)2 = ?
(a) (a– 62) (6)(a? – 62)
(c)(a? – 62) (d) (a2-624
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Answer:
We have, psinθ+qcosθ=a ...(1)
and pcosθ−qsinθ=b ...(2)
Squaring (1) and (2), and then adding, we get
(psinθ+qcosθ)
2
+(pcosθ−qsinθ)
2
=a
2
+b
2
⇒p
2
(1)+q
2
(1)−a
2
−b
2
=0⇒(p
2
−a
2
)+(q
2
−b
2
)=0
⇒(p+a)(p−a)+(q+b)(q−b)=0⇒
q+b
p+a
+
p−a
q−b
=0
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