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Q.

If asin2x+bcos2x=c,bsin2y+acos2y=d and atanx=btany then a2b2=

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a

(a−d)(c−a)(b−c)(d−b)

b

(b−c)(b−d)(a−c)(a−d)

c

(b−c)(d−b)(a−d)(c−a)

d

(d−a)(c−a)(b−c)(d−b)

answer is A.

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Detailed Solution

asin2x+bcos2x=c devide with cos2x ⇒atan2x+b=csec2x⇒(a−c)tan2x=c−b⇒tan2x=c−ba−csimilarly tan2y=d−ab−d but atanx=btany⇒a2b2=tan2ytan2x
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