Prove that the following statements are identities a...

Prove that the following statements are identities: (a) (sin heta +cos heta )^(2)=1+2sin heta *cos heta (c) (1)/(1-cos heta )+(1)/(1+cos heta )=(2)/(sin^(2) heta ) (b) (1)/(tan heta )=(cos heta )/(sin heta ) (d) tan(90deg - heta )=(1)/(tan heta ) Find the general solution of each of the following equations: (a) cos2 heta =0,4 (b) 5sin heta +14cos heta =0 Solve for x if sin(x+30deg )=-0,2 where xin(-180deg ;0deg ) 8 (c 1-cos01+cos0sin0 1 Solve for x if sin(x+30)= -0,2 where x(-180;0) acos20=0,4(b5sin0+14cos0=0 (a)(sin0+cos0=1+2sin0.cos0 Find the general solution of each of the following equations: V6.Prove that the following statements are identities: dtan90-0=- b tan0 sin0 cos0 1 tan 1

Transcript

00:01 Okay, so for part one, you had to prove that 1 minus sine squared equals cosine squared.

00:14 So they wanted you to do that with x as and r's.

00:18 So this is my x, this is my y, this is my radius.

00:22 And sine is your opposite over your hypotenuse.

00:26 So my opposite from my theta is my y and my hypotenuse is r.

00:32 And cosine is my adjacent over my hypotenuse.

00:37 So it gives me 1 minus y squared over r squared equals x squared over r squared.

00:47 And then if you simplify that, that's r squared minus y squared over r squared.

00:59 And let me move this down a little bit.

01:08 Okay.

01:10 So then i'm going to simplify this.

01:12 And your r squared, just from pythagrin theorem, is x squared plus y squared.

01:18 So then minus y squared over r squared is x squared over r squared.

01:24 And then those cancel.

01:26 So now you're left with x squared or r squared.

01:32 So you've proven that one side equals the other.

01:35 So that's the first part.

01:38 Then question number two, so let's move down a little.

01:41 Question number two is sine squared plus cosine squared plus sine squared plus sine squared, plus sine squared over cosine squared.

01:58 That equals secant over cosine.

02:04 So we're going to go through sine square plus cosine squared from your pythagorean identities is one plus sine squared over cosine squared.

02:15 Get common denominator, so this is cosine squared over cosine squared.

02:22 Plus sine squared over cosine squared.

02:28 So we're not touching the radiant side because we're trying to prove that one side equals the other.

02:35 And again, pythagorean identity, this equals 1 over cosine squared.

02:42 And i can write this as 1 over cosine times 1 over cosine.

02:49 And that gets me to, this is a secant, this is a 1 over cosine.

03:00 And you end up with secant over cosine, which matches what you had over here, which was secant over cosine.

03:14 So that's question number two.

03:16 Then question number three, okay, as you do cosine, oops, times sine of 90 minus x, plus your sign times cosine of 90 minus x, plus your sign times cosine of 90 minus.

03:46 X and you had to prove it equals to 1.

03:50 So if you know your co -function identities, move this down a little bit, okay, this is equal to cosine, cosine, and cosine and 90 minus x is sine, and then cosine times cosine is cosine squared, sine times sine is sine squared.

04:21 And from your pythagorean identities, sine square plus cosine squared is one...

Question

Please give Ace some feedback