Question

Can someone help me, please? I'm getting nowhere with this...

Consider sin x = 2/3 and 0 < x < pi/2, what's the value of (sec x + cosec x)/(1 + tan x) ?

a) 1,5
b) 4/3
c) 1,25
d) 1
e) 0,75

I reached a point where 1/cos x + 9/4cos x + 3 but I don't know what to do anymore

Answer 1

Are you allowed to use a calculator?

Answer 2

No

Answer 3

Here's what I would do. Use the fact that sin(x) = 2/3 to draw a right triangle and label the opposite side and the hypotenuse. Then find the length of the third side.

Now, looking at that triangle, use the definitions of the trig functions to fill in your equation.

Answer 4

I got approx 1.9, it didn't work

Answer 5

You did something wrong. Show me your work and I might be able to point out your mistake.

Answer 6

is that wrong?

Answer 7

Correct so far =) So maybe you made a mistake in using the trig functions, or else you simplified things wrong.

Answer 8

sec = H/A
cosec = H/O
tan = O/A

Answer 9

I got an even more nonsense answer now lol

Answer 10

Are you sure it is right to assume sqrt5, 2 and 3 only by sin x = 2/3? cuz other values could fit as well

Answer 11

Right, but the ratios woulds still work out the same.