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Given 10 sin⁴α + 15 cos⁴α = 6, find the value of 27 cosec⁶α + 8 sec⁶α.

A50
B125
C250
D75
Answer & Solution
Correct answer: C. 250
1. Let s = sin²α, c = cos²α with s + c = 1. The condition 10s² + 15c² = 6 is solved by s = 3/5, c = 2/5 (since 10·9/25 + 15·4/25 = 90/25 + 60/25 = 6). 2. cosec⁶α = 1/s³ = (5/3)³ = 125/27, so 27 cosec⁶α = 125; sec⁶α = 1/c³ = (5/2)³ = 125/8, so 8 sec⁶α = 125. 3. Sum = 125 + 125 = 250. _Source: RRB Group D CEN-02/2018 PYQ, Q.49._
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