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C2 maths help

show that (2 - cos^2 x) / (1 + sin^2 x) is equal to 1

I have substituted cos^2 x by (1 - sin^2 x) but I don't know what to do next

Reply 1

Hshshsjssnsns

what past paper is this from?

Reply 2

XavierD

Original post by man111111

show that (2 - cos^2 x) / (1 + sin^2 x) is equal to 1

I have substituted cos^2 x by (1 - sin^2 x) but I don't know what to do next

Hi,

I did for LHS:

(2 - cos^2 x) / (1+ 1 - cos^2 x)

So, (2 - cos^2 x) / ( 2 - cos ^2 x)

which equals 1

If you substitute cos^2 x by (1 - sin^2 x):

[ 2 - (1 - sin^2 x)] / (1 + sin^2 x)

So, ( 1 + sin^2 x ) / (1+ sin^2 x )

Reply 3

man111111

Original post by XavierD

hi thanks for replying,
I don't understand why [2 - (1 - sin^2 x)] gives you 1+sin^2x

In addition, I don't understand why [1+ (1 - cos^2 x)] gives you 2 - cos^2 x

Reply 4

rickH123

u need the rule

sin²x + cos²x = 1

so we got
2-cos²x / 1+ sin²x

we can substitute cos²x with 1-sin²x so we would get

2 - (1-sin²x)/1+sin²x {I think u forgot that u have to put brackets in}

so we would then get

2 - 1 + sin²x / 1 + sin²x

which equals to

1 + sin²x / 1 + sin²x

which then equals to
1

I think u forgot the fact that you had to put the 1 - sin²x inside a bracket.

Reply 5

XavierD

Original post by man111111

hi thanks for replying,
I don't understand why [2 - (1 - sin^2 x)] gives you 1+sin^2x

In addition, I don't understand why [1+ (1 - cos^2 x)] gives you 2 - cos^2 x

I just opened the brackets,

for: 2 - ( 1 - sin^2 x)

equals: 2 - 1 + sin^2 x

so, 1 +sin^2 x

for: 1 + ( 1 - cos^2 x)

opening the brackets: 1 + 1 - cos^2 x

so, 2 - cos^2 x

Please let me know if this helps :smile: