Question

If cos(2x) – a sinx = 2a – 7 has a solution for a ∈ [p, q] and r = tan9° + tan63° + tan81° + tan27°, then p.q. r = ?

(1) 40√5 

(2) 32√5 

(3) 30√5 

(4) 48√5

Answer 1

Correct option is (4) 48√5

2(sin² x – 4) + a(sinx + 2) = 0 

2(sinx – 2) + a = 0 

⇒ a = 4 – 2 sinx 

a ∈ [2, 6]