Step-by-step explanation:
To prove :
( 1 - sin x ) ( 1 + sin x ) = sec² x
LHS : -
( 1 - sin x ) ( 1 + sin x )
Formula / Identity : -
( a - b ) ( a + b ) = a² - b²
Here,
a = 1
b = sin x
( 1 - sin x ) ( 1 + sin x )
= 1 - sin² x
Identify : -
sin² θ + cos² θ = 1
cos² θ = 1 - sin² θ
Similarly,
1 - sin² x
= cos² x
= RHS
Hence verified.
Total length of the string =
yard
Length of string used for craft =
of total length of string
=
of 
= 
=
yard
Length of the string left after use = Total length of the string - Length of string used for craft
Length of the string left after use = 
=
Reducing it to the lowest term, we get
=
yard
Therefore, the length of string left is
yard.
Answer:
the expression is not factorable with rational numbers.
System A has ONE real solution
System B has NO real solutions
System C has ONE real solution