i have no idea how to do these four problems please help me!!!

1.cos 2 x= cotx - tanx

sinx cosx

2. (cosx-sinx)^2 = 1 - sin 2 x

3. secx - sinxtanx = cosx

4. cos(x+y)cosy + sin(x+y) sin y = cosx

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- Mar 16th 2006, 02:05 PMmilkywayioProving Indentity
i have no idea how to do these four problems please help me!!!

1.__cos 2 x__= cotx - tanx

sinx cosx

2. (cosx-sinx)^2 = 1 - sin 2 x

3. secx - sinxtanx = cosx

4. cos(x+y)cosy + sin(x+y) sin y = cosx - Mar 16th 2006, 02:20 PMThePerfectHackerQuote:

Originally Posted by**milkywayio**

Express as,

Double angle for,

Thus,

For Right Hand Side,

Use reciprocal identities to get,

Add fractions,

Use double angle for cosine,

Express as,

Use double angle for sine,

Use identities,

Thus, the left hand and the right hand give the same result

Q.E.D. - Mar 16th 2006, 02:23 PMThePerfectHackerQuote:

Originally Posted by**milkywayio**

Notice, that

and

Thus,

Q.E.D. - Mar 16th 2006, 02:28 PMThePerfectHackerQuote:

Originally Posted by**milkywayio**

Express, secant through cosine,

Thus, add fractions

Notice that

Thus,

Thus,

Q.E.D. - Mar 16th 2006, 02:32 PMThePerfectHackerQuote:

Originally Posted by**milkywayio**

Thus,

Notice that this is the cosine for difference of two angles, thus,

Substitute that value of thus,

Thus,

Q.E.D.