If 15sin^4α +10cos^4α = 6, for some α ∈ R, then the value of 27sec^6α + 8cosec^6α is equal to :

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Takshii · Answer 1 · 2021-03-27T08:13:49+0000

Correct option is (4) 250

15sin⁴α + 10cos⁴α = 6

15sin⁴α + 10cos⁴α

= 6(sin²α + cos²α)²

(3sin²α – 2cos²α)² = 0

tan²α = \(\frac 23.\) cot²α = \(\frac 32\)

⇒ 27sec⁶α + 8cosec⁶α

= 27(sec⁶α )³ + 8(cosec⁶α )³

= 27(1 + tan²α )³ + 8(1 + cot²α)³

= 250