Question

the Alpha is the measure of an acute angle and 3 sin alpha equals to 2 cos alpha prove that (1- tan² alpha/1+tan² alpha)² +(2 tan alpha/1+tan²alpha)² equal to 1.

Answer 1

Here in the first step,
cos alpha is taken to the Left side, so it is at the denominator
and 3 goes to the Right hand side in the denominator.
sin alpha /cos alpha is tan alpha.
=>tan alpha =2/3
Using this tan alpha put in other equation to get required result,as shown in above solution.

Hope you understand.