Question

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​

Answer 1

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