if A and B are acute angles and sinA=cosB,prove that A+B=90degrees

plz help me

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- September 11th 2006, 12:25 AMsanya.batratrigonometry
if A and B are acute angles and sinA=cosB,prove that A+B=90degrees

plz help me - September 11th 2006, 01:27 AMTD!
sin(a) = cos(b)

sin(a) = sin(pi/2-b)

a = pi/2-b <=>**a+b = pi/2**

OR

a = pi-(pi/2-b) <=> a = pi/2+b <=> a-b = pi/2

If a and b are positive and acute, the bold answer is the only one remaining. - September 11th 2006, 01:36 AMzanyzanny
Please see attached I hope this makes sense.

- September 11th 2006, 02:27 AMQuick
- September 11th 2006, 02:48 AMzanyzanny
- September 11th 2006, 03:22 AMCaptainBlack
Please try to avoid the use of proprietary file formats in attachments,

not everybody can read them in their native application which can result

in some unpleasant effects.

I would usually favour turning anything less than about 1 page into

a graphics format. I would recommend .png, but this site imposes a size

limit on .png files so in practice a high quality .jpg seems to work best.

RonL - September 11th 2006, 04:27 AMzanyzanny
Wow I have no idea what you just said or how you did that! :confused: :o

It looks good though.:)

Sorry I was just trying to be helpful. I don't have much idea about formats and stuff like that I am mostly interested in the maths :D - September 11th 2006, 06:07 AMGlaysher
Basically just do it in Paint. It gives you the option to save as a png file or a jpg file when you do Save As.

- September 11th 2006, 08:49 AMSoroban
Hello, sanya.batra!

Here's a roundabout approach . . .

Quote:

Of A and B are acute angles and sin A = cos B,

prove that: A + B = 90°

We are given: .cos B .= .sin A .**[1]**

Square both sides: .cos²B .= .sin²A

Subtract from 1: .1 - cos²B .= .1 - sin²A

And we have: .sin²B .= .cos²A

Since A and B are acute: .sin B = cos A .**[2]**

Now consider: .sin(A + B)

. . . . . . . . . We have: .sin(A + B) .= .sin(A)·cos(B) + sin(B)·cos(A)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .↓ . . . . . ↓

Substitute [1] and [2]: .sin(A + B) .= .sinA·sin(A) + cos(A)·cos(A)

Hence: .sin(A + B) .= .sin²A + cos²A . → . sin(A + B) .= .1

Therefore: .**A + B .= .90°**

(Recall that A and B are both*acute*angles.)

- September 11th 2006, 08:58 AMCaptainBlack
Produce the diagrams and text in any application you like.

Display them on the screen, then alt-PrintScreen will capture

the active window to the system clipboard. Open a graphics

application and paste, or paste-as-new to paste the clipboard

image into the application, crop to include only what you want

in the final image, then resize and save in favourite format.

Upload saved image file just like any other file and its done.

RonL