Thursday

October 23, 2014

October 23, 2014

Posted by **Amy** on Saturday, March 19, 2011 at 8:57am.

could someone explain or write down steps on how the left side becomes 1?

- Math -
**Reiny**, Saturday, March 19, 2011 at 9:04amI am positive that you meant that to type

sin^2x + cos^2x =1

label a right angled triangle having sides a, b, and c

with c as the hypotenuse and angle Ø opposite side a.

LS = sin^2Ø + cos^2Ø

= (a/c)^2 + (b/c)^2

= (a^2/c^2) + (b^2/c^2)

= (a^2 + b^2)/c^2 , but a^2 + b^2 = c^2 by Pythagoras

so

LS = c^2/c^2

= 1

= RS

(the choice of variable does not matter, you can call your angle Ø or x or whatever)

- Math -
**Amy**, Saturday, March 19, 2011 at 9:06amthe original problem was:

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

- Math -
**Reiny**, Saturday, March 19, 2011 at 12:04pmIn that case you expanded it incorrectly, should have been

LS

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

= sin^2x + 2sinxcosx + cos^2x + sin^2x - 2sinxcosx + cos^2x

= sin^2x+cos^2x + sin^2x + cos^2x

= 1+1

= 2

= RS

**Answer this Question**

**Related Questions**

Math - Calculus - The identity below is significant because it relates 3 ...

trig - it says to verify the following identity, working only on one side: cotx+...

Trigonometry - I need to prove that the following is true. Thanks. csc^2(A/2)=...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...

algebra - Can someone please help me do this problem? That would be great! ...

trig - The expression 4 sin x cos x is equivalent to which of the following? (...

math - Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t...

Limit Calculas - Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. ...

calculus - Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am ...

tigonometry - expres the following as sums and differences of sines or cosines ...