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.
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
Hello, sanya.batra!
Here's a roundabout approach . . .
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.)
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