Verify the identity
cosx/1+sinx + 1+sin/cosx = 2sec x

Ill assume its  the first one.

cos x / ( 1 + sin x)  + (1 + sinx ) / cos x

=   cos^2 x + (1 + sin x)^2 / cos x (1 + sin x)

=  cos^2 x + sin^2x + 1 +  2sinx / cos x( 1 + sin x)

=  1 + 1 + 2sinx / cos x( 1 + sin x)            (because sin^2x + cos^2 x = 1)

= 2 (1 + sin x ) /  cos x(1 + sin x)   = 2 / cos x   =   2 sec x

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

(-0, -7) is your answer