Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2) / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B ) - correct
Answer:
C. 7.8
Step-by-step explanation:
This problem involves the use of a trigonometric ratio. This one specifically involves the use of cosine as it provides the leg adjacent to the angle and the hypotenuse.
cos(40) = 6/x
cos(40)*x=6/x*x
cos(40)*x=6
cos(40)/cos(40)*x=6/cos(40)
x=6/cos(40)
x=7.83
The value of x is C. 7.8
Step-by-step explanation:
The formula for the circumference of a circle is 2*pi*radius
Circumference = 2(3.14)(2.1)
= 13.188cm
Simplify by dividing a common factor (5). 15/24. Check to see if it can be simplified. Repeat (using 3). 5/8. Check to see if it can be simplified. It can't, so the answer is 5/8
