Question

find all solutions in interval [0, 2pi) in: secB cscB = 2cscB

Answer 1

Rule of Thumb: When in doubt, change everything to sine and cosine.

Answer 2

1/cosB 1/sinB = 2 1/sinB

Answer 3

sinBcosB/cosBsinB=2/sinB

Answer 4

1=2/sinB

Answer 5

am I on the right track here?

Answer 6

Don't be dividing by stuff. FACTOR!

secB cscB = 2cscB

secB cscB - 2cscB = 0

(secB - 2)cscB = 0

csc(B) = 0. Does that ever occur?

sec(B) = 2 or 1/cos(B) = 2 or cos(B) = 1/2 <== That's better.

Answer 7

OMG, that is so simple. Why can't I see that? Crazy! Thanks!

Answer 8

No worries. Lots of folks panic when they see something besides sine, cosine, and tangent. Keep working at it. You'll get it.