Question

help me pleaseeeeeeeeeeeeeeeeeeeeee..
if sin A + Sin^2 A = 1, find the value of:
(1) sin A (2) cos^2 A + 2 cos^4 A.

Answer 1

1) SINA( 1+ SINA) =1
SO SINA = 1 SINA=0
A= 90 A= 180 ,0

Answer 2

i did that.. that is not the answer that they want..i have the answer actually.. the answer for (1) is \[(-1+\sqrt{5}) \div 2\]

Answer 3

i have all the answer but i don't know how to do..

Answer 4

Use Quadratic equation here..

Answer 5

\[\sin^2(A) + \sin(A) - 1 = 0\]

a = 1, b= 1 and c = -1

Find Discriminant here:



\[D = b^2 - 4ac = 1 + 4 = 5\]

\[\sqrt{D} = \sqrt{5}\]

\[\sin(A) = \frac{-b \pm \sqrt{D}}{2a}\]

\[\sin(A) = \frac{-1 \pm \sqrt{5}}{2}\]

Answer 6

Getting @SyaIE

Answer 7

ohhhhhhhhhhhhhhhhhhh!! i get it!! thank you~ :)

Answer 8

Can you tell me answer of your Second Part..

Answer 9

YES YOU ARE RIGHT ITHINK YOU WANT FIND A
SORY

Answer 10

@obada its okay.. thanks anyway..

answer for (2) is \[(5+\sqrt{5}) \div 2\]

Answer 11

Are you able to do second part ??

Answer 12

ermm.. not really..
im still doing it..

Answer 13

Think like this:

\[\cos^2(A) + 2 \cos^4(A) \implies \cos^2(A)(1 + 2\cos^2(A))\]

I am still thinking how to do easily..

So give me sometime..

Answer 14

what i did was\[1-\cos ^{2} A + (1-\cos ^{2})^{2} =1\]
then i expand the \[(1-\cos ^{2} A)^{2}\]..
now im stuck

Answer 15

Hey you have solved it..

I think you did not get how I tell you..

Answer 16

yeah.. i don't get it, i guess.. hihi

Answer 17

@waterineyes gooooood teacher

Answer 18

See:

\[(1 - \sin^2(A)) + 2(\cos^2(A))^2 \implies (1 - \sin^2(A)) + 2(1 - \sin^2(A))^2\]

\[\implies (1- \sin^2(A))(1 +2(1-\sin^2(A))) \implies (1 - \sin^2(A)) \times (3 - 2\sin^2(A))\]

Answer 19

Give me some more time..

Now I am also stuck..

Answer 20

We have to convert that cos terms into sin so that we can use the given..

So let me try first..

Answer 21

okie~:)

Answer 22

I am close but I am trying now also to get the right answer..

Answer 23

i think im about get the answer.

Answer 24

See we are given with:

\[\sin(A) + \sin^2(A) = 1\]

So:

\[\sin(A) = 1 - \sin^2(A) = \cos^2(A)\]

Till here you got??

Answer 25

\[1 - \sin^2(A) = \cos^2(A)\]

This is the basic identity..

Getting??

Answer 26

So we have:

\[\sin(A) = \cos^2(A)\]

Answer 27

yup..

Answer 28

\[\cos^2(A) + 2(\cos^2(A))^2 \implies \sin(A) + 2\sin^2(A)\]

Getting till here..

Answer 29

Having any problem till here?/ @SyaIE

Answer 30

no problem..i get it.. :)

Answer 31

Can you go forward now on your own??

Answer 32

You can write it as:

\[\sin(A) + 2\sin^2(A) = \color{green}{(\sin(A) + \sin^2(A))} + \sin^2(A)\]

\[\implies 1 + \sin^2(A)\]

Answer 33

alright...

Answer 34

So to find \(sin^2(A)\)

You have sin(A) = :

\[\sin(A) = \frac{-1 + \sqrt{5}}{2}\]

Square it:

\[\sin^2(A) = \frac{1 + 5 + 2 \sqrt{5}}{4} \implies \frac{3+ \sqrt{5}}{2}\]

Add it to 1 now and you will have your answer..

Answer 35

yupp!!.. i get it.. but.. i got.\[(3-\sqrt{5})\div2\]

Answer 36

Or you can have this also:

\[\sin^2(A) = \frac{1 + 5 - 2 \sqrt{5}}{4} \implies \frac{3- \sqrt{5}}{2}\]

Answer 37

Well Done..

Answer 38

See:

\[1 + \frac{3 - \sqrt{5}}{2} \implies \frac{2 + 3 - \sqrt{5} }{2} \implies \frac{5 - \sqrt{5}}{2}\]

Answer 39

yeah.. i get it~.. THANK YOU SOOOOOOOOOOOOOOOOOOOO MUCH..:)

Answer 40

So your answer will be both:

\[\frac{5 \pm \sqrt{5}}{2}\]

Answer 41

YUP..

Answer 42

Welcome dear..