10sin4x+15cos4x=6⇒10sin4x+15cos4x=6×(1)2⇒10sin4x+15cos4x=6(sin2x+cos2x)2
Dividing both sides by cos4x we get
⇒10tan4x+15=6(tan2x+1)2⇒4tan4x−12tan2x+9=0⇒(2tan2x−3)2=0⇒tan2x=32⇒cot2x=23
Now,
24sec6x−27 cosec6 x=24(sec2x)3−27( cosec2 x)3=24(1+tan2x)3−27(1+cot2x)3=24(52)3−27(53)3=53(3−1)=250