Question

Solve sin^2x = cos^2x

Answer 1

hint : sin^2 (x) = 1- cos^2 x

Answer 2

and cos^2 (x) + sin^2 (x) = 1

ANOTHER HINT!!

Answer 3

OMG so many hints :)

Answer 4

The 2nd is just a rip-off of the first. :-P

Answer 5

Hints don't help when you have no idea what you're doing O.o

Answer 6

lolol.

Answer 7

Use your identities.

Answer 8

well!!! you need to know your identities mr.!! :P

Answer 9

can I be "Isuckatmath9998"?

Answer 10

It's not even true, I'm pretty good at math, I just have a horrible teacher xD

Answer 11

I'd be "isuckatmath10000000" because I suck at it a little too much.

Answer 12

noooo don't blame the teacher xD

Answer 13

It's an online course, we literally have like nothing to reference

Answer 14

there are some horrible teachers out there :/

Answer 15

OK you have

sin^2 (x) + cos^2 (x) = 1 RIGHT??

Answer 16

@isuckatmath9999 You have the whole internet.

Answer 17

1/2= cos(x)^2 can you do that?

Answer 18

Here I'll get you started:
\[\sin^2x=(1-\sin^2x)\]

Answer 19

WTH IS 1/2 = COS ^ (X)?

Answer 20

zz made a booboo

Answer 21

lol??? tell me more about this identity. :)

Answer 22

I feel like this is counterproductive

Answer 23

wait..

Answer 24

zz pulls identities out of his butt.

Answer 25

\[\sin^2(x) = \dfrac{1}{2} \Rightarrow \sin(x) = \pm \frac{1}{\sqrt{2}}\]

Answer 26

can you elaborate....because im confused now. :|

Answer 27

sin(x)^2 = cos(x)^2 imples cos(x)^2 = 1-cos(x)^2 imples 2cos(x)^2 = 1 imples cos(x)^2 = 1/2

Answer 28

there are two ways to solve this

Answer 29

Should be 2 solutions.

Answer 30

do we have any restrictions?

Answer 31

infinite solutions

Answer 32

@Luigi0210 what I do wrong?

Answer 33

0 ≤ x ≤ 2π

Answer 34

Two different solutions in the interval \(0 \le x < 2\pi\)

Answer 35

Ugh is it
\[\sin^2x = \cos^2x\]
why not just
\[\tan^2x=1\]?
then
\[tanx= \pm 1\]

Answer 36

we are all saying the same thing......

Answer 37

Nothing, sorry about that zz ^_^'

Answer 38

ha, math is fun .-.

Answer 39

x = (pi)n/2-pi/4

Answer 40

pick n according to restrictions...

Answer 41

Let'sall stick with @Mr. Kohli's and @zzr0ck3r 's methods.....

Answer 42

I think @.sam was the best

Answer 43

@.Sam.

Answer 44

Indeed, I didn't think of what .Sam. said :P

Answer 45

There will be 4 solutions
x=45
x=180-45=135
x=180+45=225
x=360-45=315

Answer 46

Tbh i havent even seen what Sam said, looking now .lol.

Answer 47

Oh

Answer 48

Oh wow. I see. But does @isuckatmath9999 understand @.Sam.'s method?

Answer 49

Yes i do that really helped :)

Answer 50

\[\sin^2x=\cos^2x \]
Divide both sides by \(cos^2x\)
\[\frac{\sin^2x}{\cos^2x}=1\]
Using
\[tanx=\frac{sinx}{cosx}\]
So
\[\tan^2x=1\]
Square roo both sides
\[\tan(x)= \pm 1\]
Then use the the diagram (forgot what it's called) for tangent

Since it's \(\pm 1\) you'll have 4 solutions, but sometimes it doesnt, you'll have to be careful for that

Answer 51

Awesome