Practicing Success
If $4 \sin ^2(2 x-10)^{\circ}=3,0 \leq(2 x-10) \leq 90$, then find the value of $\frac{\sin ^4(x-5)^{\circ}+\cos ^4(x-5)^{\circ}}{1-2 \sin ^2(3 x-15)^{\circ} \cos ^2(3 x-15)^{\circ}}$. |
$\frac{5}{8}$ -1 1 $-\frac{5}{8}$ |
$\frac{5}{8}$ |
We are given that , 4 sin² ( 2x - 10 )º = 3 sin² ( 2x - 10 )º = \(\frac{3}{4}\) sin ( 2x - 10 )º = \(\frac{√3}{2}\) { we know, sin60º = \(\frac{√3}{2}\) } So, ( 2x - 10 )º = 60º x = 35º Now, \(\frac{sin4 (35-5)º + cos4 ( x - 5 )º }{1 - 2sin²(3x-15)º . cos²(3x-15)º }\) = \(\frac{sin4 (35-5)º + cos4 ( 35 - 5 )º }{1 - 2sin²(105-15)º . cos²(105-15)º }\) = \(\frac{1/16 + 9/16 }{1 }\) = \(\frac{10 }{16 }\) = \(\frac{5}{8}\) |