Posted by **lungisile ntobela** on Sunday, January 22, 2012 at 4:10pm.

how do you solve this.prove: cos2A plus cosA divided by sin2A minus sinA equal to cos2A plus 1 divided by sinA

- math -
**Steve**, Sunday, January 22, 2012 at 5:16pm
I think there's a typo in your equation. For example , plug in A = pi/4. You then have

(0 + 1/√2)/(1 - 1/√2) = (0+1)/(1/√2)

1/√2 *√2 /(√2 - 1) = √2

1/(√2-1) = √2

√2+1 = √2

However, if you fix the right side to read (cosA+1)/sinA

you have the left side:

(cos^2 A - sin^2 A + cosA)/(2sinAcosA - sinA)

(cos^2 A - (1 - cos^2 A) + cosA)/(2sinAcosA - sinA)

(2cos^2 A + cosA - 1)/[sinA(2cosA - 1)

(2cosA-1)(cosA - 1)/[(2cosA - 1)(sinA)]

(cosA -1)/sinA

Now if you plug in any angle, the equality holds.

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