Question

sec Square X by 2 by 2 tan x by 2

Answer 1

cosec x is the answer. break in sin cos simplyfy it. in the denominator part we will get the sinx so 1/sinx is cosec x which is the answer

Answer 2

we have to find out value of $\frac{sec^2\frac{x}{2}}{2tan\frac{x}{2}}$

first of all, we have to replace 1/cos²x/2 in place of sec²x/2 and 2sinx/2/cosx/2 in place of 2tanx/2

$=\frac{\frac{1}{cos^2x/2}}{2\frac{sinx/2}{cosx/2}}$

$=\frac{1}{2sinx/2.cosx/2}$

we know, 2sinA.cosA = sin2A

so, 2sinx/2 .cosx/2 = sinx

= $\frac{1}{sinx}$

=$cosecx$