arcsinx-arccosx = 0

i know x is 45

but how to do algebraccly

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- Sep 18th 2010, 06:03 AMaeroflixsolved algebracially
arcsinx-arccosx = 0

i know x is 45

but how to do algebraccly - Sep 18th 2010, 06:20 AMsa-ri-ga-ma
Check the problem.

If sinx - cosx = 0 then x = 45 degrees.

Now

arcsinx+arccosx = π/2

arcsinx-arccosx = arcsinx+arccosx - 2arcosx = 0

π/2 -2arccosx = 0

Solve for x. - Sep 18th 2010, 07:34 AMSoroban
Hello, aeroflix!

Quote:

Solve: .

i know x is 45 . . This is wrong!

.[1]

.[2]

The equation becomes: .

Take the sine of both sides: .

and we have: .

Substitute [1] and [2]: .

. .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I tried tomy answers and ran into a new puzzle.*check*

. . (New to*me*, anyway.)

First, I assumed that the angles are in

Then I tested

We have: . .Does it equal 0 ?

We know that: .

So we have: .

The equation is true**if**we select from both sets.

Query: .*Are we allowed to do that?*