Let the set of all a ∈R such that the equation cos ⁡2x+a sin ⁡x=2a-7 has a solution be [p ,q ] and r= tan ⁡9^ - tan ⁡27^ - 1 cot ⁡63^ + tan ⁡81^ , then pqr is equal to_____

Question

Accepted Answer

Correct answer: 48. (48) cos ⁡2x+a sin ⁡x=2a-7a ( sin ⁡x-2 )=2 ( sin ⁡x-2 ) ( sin ⁡x+2 ) sin ⁡x=2 , a=2 ( sin ⁡x+2 ) ⇒a ∈ [2 ,6 ]p=2q=6 r= tan ⁡9^ + cot ⁡9^ - tan ⁡27- cot ⁡27r= math1 sin ⁡9 cos ⁡9- man ⁡1 sin ⁡27 cos ⁡27=2( 4 5-1- 4 5+1)r=4p .q .r=2 6 4=48

$Let the set of all a \in R such that the equation cos 2 x + a sin x = 2 a - 7 has a solution be [p, q] and r = tan 9^{\circ} - tan 27^{\circ} - \frac{1}{cot 63 ^{\circ}} + tan 81^{\circ}, then pqr is equal to_____$

Solution

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