Question

prove (1-sin x)/sec x = cos^3 x/1+sin x any trig people in the houseeeeee

Answer 1

On LHS, replace 1/sec(x) with cos(x).
Multiply top and bottom of LHS by (1 + sin(x)) and simplify to get the RHS.

Answer 2

i have actually solved this working with both sides of the equation i just got lost in the steps a little bit so i was hoping someone could rework it

Answer 3

=(12−sin2x)1cosx(1+sinx)
=cos2x×cosx(1+sinx)=cos3x1+sinx

Answer 4

how did we get this?

Answer 5

\[\frac{ 1-\sin(x) }{ \sec(x) } = (1 - \sin(x))\cos(x) = (1 - \sin(x))\cos(x) \times \frac{ (1+\sin(x)) }{ (1 + \sin(x)) } = ?\]

Answer 6

i have this all typed up i am sorry it wont copy and paste right

Answer 7

(1^2−sin^2x)/(1/cosx)(1+sinx)

Answer 8

(1 - sin(x)) * (1 + sin(x)) = 1^2 - (sin(x))^2 (because (a-b)(a+b) = a^2 - b^2
1^2 - (sin(x))^2 = cos^2(x)

Answer 9

then multiply both sides buy cosx to eliminate that sec in the demoninator

Answer 10

oh i think thats what i needed!

Answer 11

(1^2−sin^2x)/(1/cosx)(1+sinx) = cos^2(x) / { 1 / cos(x) * (1 + sin(x)) } =
cos^3(x) / (1 + sin(x))

Answer 12

i get it, its the algebra that kills me like that.

Answer 13

alright.

Answer 14

great thanks!

Answer 15

any last words of wisdom ill take from you haha

Answer 16

You are welcome.
Dividing by a fraction is same as multiplying by its reciprocal. Here dividing by (1/cos(x)) is same as multiplying by cos(x).