Question

Prove that the given equation is an identity

Answer 1

\[(1+\cot ^2x)(1-\cos2x)=2\]

Answer 2

How would you approach this?

Answer 3

48-12=36
3*36=108
when dad be 108 years old he is 3 times older than his son .

Answer 4

sri :
y-x=36
y=3x
2x=36
x=18
y=54

Answer 5

Try expanding the brackets.

Answer 6

i made a mistake .

Answer 7

And remember\[\cos2x=\cos^2x-\sin^2x=2\cos^x-1=1-2\sin^2x\]

Answer 8

\[(\csc^2x)(1-(1-2\sin ^2x))=\csc ^2x(2\sin ^2x)=\frac{1}{\sin ^2x}(2\sin ^2x)=1\]

Answer 9

I mean = 2. Sorry for the typo

Answer 10

Or just give them the answer, sure why not...

Answer 11

Well, the first question is solved anyways. So I guess it doesn't matter.

Answer 12

oh.

Answer 13

I'm a bit confused on how\[\cos2x=1-2\sin^2x\]

Answer 14

I know how \[\cos^2x=1-\sin^2x\]

Answer 15

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

Answer 16

\[\cos2a=\cos^2a-\sin^2a\]This is one of the trigonometric identities. Or more generally,\[\cos(a \pm b) =cosa*cosb \mp sina*sinb\]You already know that\[\cos^2a=1-\sin^2a\]Substitute for cos²a\[\cos2a=(1-\sin^2a)-\sin^2a=1-2\sin^2a\]

Answer 17

Right! I completely forgot about that identity. Thank you very much!

Answer 18

No problem :)