Question

1-cosa+cos2a / sin2a-sina

Answer 1

(2cos²-cosa)/(2sinacosa-sina)=cosa(2cosa-1)/sina(2cosa-1)=cosa/sina=
=ctga

Answer 2

We can simplify the expression as follows:

1 - cos(a) + cos(2a) / (sin(2a) - sin(a))

= (1 - cos(a)) / (sin(2a) - sin(a)) + cos(2a) / (sin(2a) - sin(a))

= sin(a) / (sin(a) - sin(2a)) + cos(2a) / (sin(2a) - sin(a))

Now we can use the trigonometric identities:

sin(2a) = 2sin(a)cos(a)

cos(2a) = 2cos^2(a) - 1

to simplify the expression further:

sin(a) / (sin(a) - sin(2a)) + cos(2a) / (sin(2a) - sin(a))

= sin(a) / (sin(a) - 2sin(a)cos(a)) + (2cos^2(a) - 1) / (2sin(a)cos(a) - sin(a))

= sin(a) / sin(a)(1 - 2cos(a)) + (2cos^2(a) - 1) / sin(a)(2cos(a) - 1)

= 1/(1 - 2cos(a)) + (2cos(a) - 1)/(sin(a)(2cos(a) - 1))

= (1 + sin(a))/(sin(a)(2cos(a) - 1))

Therefore, the simplified expression is (1 + sin(a))/(sin(a)(2cos(a) - 1)).