if 10sin^4x+15 cos^4x=6. prove that 27 cosec^6x+8 sec^6x=250
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10sin4x+15cos4x=6,(1)
10sin4x+15cos4x=6(sin2x+cos2x)2
10sin4x+15cos4x=6sin4x+12sin2xcos2x+6cos4x⟹
4sin4x−12sin2xcos2x+9cos4x=0
(2sin2x−3cos2x)2=0⟹
2sin2x−3cos2x=0
2cos2x=3sin2x=2+3cos2x+sin2x=5⟹
2sec2x=3csc2x=5
27csc6x+8sec6x=125+125=250
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