Question

(1-sinx)/cosx=cosx/(1+sinx)

verify

Answer 1

"cross multiply" and get
\[1-\sin^2(x)=\cos^2(x)\] which is true

Answer 2

but you have to prove it by changing only 1 side of the equation

Answer 3

Try multiplying numerator and denominator on the left side by the numerator's conjugate (1 + sin x)

Answer 4

ok you get, 1-sinx^2/cosx(1+sinx)

Answer 5

That's right. Now look at the numerator and apply Satellite's first post.

Answer 6

of cross multiplication?

Answer 7

No. We did not touch the right side, just change 1 - sin^2 x to cos^2 x and reduce.

Answer 8

alright so then you get: cos^x/1+sinx, thank you sooo much!

Answer 9

help on another?

Answer 10

cos(pi/2+x) = -sin x

I just said that they inverted the signs on both sides of the orignial identity

Answer 11

expand out cos(a + b) =cos a cos b - sin a sin b

Answer 12

ok so..gimme a sec :)

Answer 13

i dont think i did right...for the first product i got cos^22xpi/2...

Answer 14

@ybarrap

Answer 15

hello :/

Answer 16

@NoelGreco?

Answer 17

unit circle?

Answer 18

The cosine of a sum is what you have to apply to the left side.

ybarrap presented it correctly just substitute x for a and pi/2 for b.

Answer 19

i did i got it guys

Answer 20

a=\(\pi\)/2, b = x

Answer 21

thank you!

Answer 22

great!

Answer 23

i frgot to refer to the unit circle to find the quantities for cos(pi/2) and sin(pi/2)

Answer 24

that helps

Answer 25

yeah :P thank you both!

Answer 26

But also remember that cos and sin equal in magnitude when shifting either by a value of pi/2, so you could have figures this out by looking at the graph of sin and cos and see what happens when you shift cos(x) \(\pi\)/2 units to the left. Then you just need to know the sign polarity to make it perfect.

Answer 27

ok :)

Answer 28

Also remember that if you see sin(x - pi/2) is simply cos x. That's because (x - pi/2) is simply the COmplement of x. That's where the "co" in cos, cot, csc comes from.

Another example cot(x - pi/2) = tan x.

Don't work harder than you have to.

Answer 29

ok :)