How do you simplify cos^2B / (1-sinB)cos2B1−sinB?

1 Answer
Alan P.
Oct 24, 2015

(cos^2(B))/(1-sin(B)) = 1+sin(B)cos2(B)1−sin(B)=1+sin(B)

Explanation:

Based on the definitions of sinsin and coscos and on the Pythagorean Theorem
color(white)("XXX")cos^2(B)+sin^2(B) = 1XXXcos2(B)+sin2(B)=1
or
color(white)("XXX")cos^2(B) = 1-sin^2(B)XXXcos2(B)=1−sin2(B)

color(white)("XXXXXXX")=(1-sin(B))*(1+sin(B))XXXXXXX=(1−sin(B))⋅(1+sin(B))

Therefore
color(white)("XXX")(cos^2(B))/(1-sin(B)) = (cancel((1-sin(B)))*(1+sin(B)))/(cancel((1-sin(B)))

Related questions
See all questions in Relating Trigonometric Functions
Impact of this question
4172 views around the world
You can reuse this answer
Creative Commons License