Answer:
Step-by-step explanation:
1.
cot x sec⁴ x = cot x+2 tan x +tan³x
L.H.S = cot x sec⁴x
        =cot x (sec²x)²
        =cot x (1+tan²x)²     [ ∵ sec²x=1+tan²x]
        =  cot x(1+ 2 tan²x +tan⁴x)
        =cot x+ 2 cot x tan²x+cot x tan⁴x
         =cot x +2 tan x + tan³x        [ ∵cot x tan x  =1]
 =1]
        =R.H.S
2.
(sin x)(tan x cos x - cot x cos x)=1-2 cos²x
  L.H.S =(sin x)(tan x cos x - cot x cos x)
           = sin x tan x cos x - sin x cot x cos x
            
            = sin²x -cos²x
            =1-cos²x-cos²x
            =1-2 cos²x
            =R.H.S
           
3.
1+ sec²x sin²x =sec²x
 L.H.S =1+ sec²x sin²x 
          = [
                       [ ]
]
          =1+tan²x                        ![[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%5Ctextrm%7Bsin%20x%7D%7D%7B%5Ctextrm%7Bcos%20x%7D%7D%20%3D%20%5Ctextrm%7Btan%20x%7D%5D)
          =sec²x
         =R.H.S
4.

L.H.S=
        
       
      
       = 2 csc x
     = R.H.S
5.
-tan²x + sec²x=1
L.H.S=-tan²x + sec²x
         = sec²x-tan²x
         =
         
         
         =1
      
        
 
        
             
        
        
        
Answer:
$38.26
Step-by-step explanation:
add the amounts together and multiply by 0.075 and 0.15 add these answers to the original amount
 
        
             
        
        
        
Answer:

Step-by-step explanation:
we know that
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
see the attached figure to better understand the problem
so
∠DEF=∠ECD+∠CDE
substitute the given values

solve for x
Combine like terms

Group terms



Find the measure of angle CDE

substitute the value of x

 
        
             
        
        
        
TOTAL IS $10
If the party costs $5 and each additional person is $1 and she invites 5 more 5 X 1 = 5
OR 1 + 1 + 1 + 1 + 1
 
        
             
        
        
        
Answer:
the equation is not correct....
well, it should look sth. like (x+or- number)^2=number