Answer:
Y<u>></u>-x-5
Step-by-step explanation:
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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:
A = 0 +/- nπ radians , where n is an integer.
Step-by-step explanation:
cos 2A = cos^2 A
Use the identity cos 2A = 2 cos^2 A -1 :
2cos^2 A - 1 = cos^2 A
cos^2 A = 1
Cos A = +/-1
When cos A = 1, A = 0 +/- 2nπ radians.
when cos A = -1, A = π +/- nπ radians.