math
posted by lungisile ntobela on .
how do you solve this.prove: cos2A plus cosA divided by sin2A minus sinA equal to cos2A plus 1 divided by sinA

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/(√21) = √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)
(2cosA1)(cosA  1)/[(2cosA  1)(sinA)]
(cosA 1)/sinA
Now if you plug in any angle, the equality holds.