Proove that tanx/secx+1 = 2cosx-2cos^2/sin2x

Answer 1

Not possible, but you can disprove it, with one counterexample. Let x = 30 degrees

tan30= 1/sqr3, sec30=2

1/sqr3/(2+1)= 1/3sqr3 for the left side

cos30 = 1/2, cos^2(30) = 1/4, sin60=sqr3/2

2cos30 = 1, 2cos^2(30)= 1/2

2cos30-2cos^2(30)/sin60 = 1-1/2/sqr3/2 = 1-1/sqr3 for the right side

1/3sqr3 =? 1- 1/sqr3 = (sqr3-1)/sqr3, cancel the sqr3 in the denominators

1/3 = ? sqr3-1

.333...does not = 1.732-1 = .732