<span>(1 + cos² 3θ) / (sin² 3θ) = 2 csc² 3θ - 1
Starting with the left:  Note that  cos²θ + </span><span>sin²θ = 1.
In the same way:    </span><span>cos²3θ + <span>sin²3θ = 1
</span></span>Therefore                cos²3θ  = 1 - <span>sin²3θ
</span> From the top:  (1 + cos² 3θ) = 1 + 1 - sin²3θ = 2 - <span>sin²3θ
</span>
(1 + cos² 3θ) / (sin² 3θ) = (<span>2 - sin²3θ) / (sin² 3θ) = 2/</span><span>sin² 3θ - </span><span>sin²3θ/</span>sin²3θ 
=  2/<span>sin² 3θ - 1;        But 1/</span><span>sinθ = csc</span><span>θ,  Similarly  </span>1/sin3θ = csc3θ
= 2 *(1/sin<span>3θ)²  - 1</span>
= 2csc²3θ  - 1.        Therefore  LHS = RHS.  QED.
        
             
        
        
        
Answer:
C. 20 feet
Step-by-step explanation:
Let x = width
Let y = length
If the length is at least 10 feet longer than the width:
⇒ x + 10 ≤ y
⇒ x ≤ y - 10
If the perimeter is to be no more than 100 ft:
⇒ 2x + 2y ≤ 100
⇒ x + y ≤ 50
⇒ x ≤ 50 - y
Equate the equations for x and solve for y:
⇒ y - 10 = 50 - y
⇒ 2y = 60
⇒ y = 30
Substitute found value of y into one of the inequalities for x:
⇒ x ≤ 30 - 10
⇒ x ≤ 20
Therefore, the maximum possible width of the fence is 20 feet.
 
        
             
        
        
        
The best buy is the 9 oz box of rice $1.25c.
        
             
        
        
        
Answer:
72/9 is equivalent to 8/1 is the answer.
Step-by-step explanation:
 
        
                    
             
        
        
        
The correct answer is 400.