To simplify this expression, we need to use the trigonometric identity:
cos A−BA - BA−B = cos A cos B + sin A sin B
Using this identity, we can rewrite the expression as:
cos 68 - cos 22 / sin 68 - sin 22 = cos68<em>cos22+sin68</em>sin22cos 68 <em> cos 22 + sin 68 </em> sin 22cos68<em>cos22+sin68</em>sin22 / sin68−sin22sin 68 - sin 22sin68−sin22
To simplify this expression, we need to use the trigonometric identity:
cos A−BA - BA−B = cos A cos B + sin A sin B
Using this identity, we can rewrite the expression as:
cos 68 - cos 22 / sin 68 - sin 22
= cos68<em>cos22+sin68</em>sin22cos 68 <em> cos 22 + sin 68 </em> sin 22cos68<em>cos22+sin68</em>sin22 / sin68−sin22sin 68 - sin 22sin68−sin22
= cos(68−22)cos (68 - 22)cos(68−22) / sin68−sin22sin 68 - sin 22sin68−sin22
= cos46cos 46cos46 / sin68−sin22sin 68 - sin 22sin68−sin22
Since cos 46 is a constant value, we can further simplify the expression by finding the values of sin 68 and sin 22:
sin 68 = sin 90−2290 - 2290−22 = cos 22 = 0.927
sin 22 = sin 22 = 0.374
Now we can substitute these values back into the expression:
= cos 46 / 0.927−0.3740.927 - 0.3740.927−0.374
= cos 46 / 0.553
= 0.718 / 0.553
= 1.301
Therefore, the value of cos 68 - cos 22 / sin 68 - sin 22 is approximately 1.301.