SSC CPO 2024 PYQ — Question 128

The correct answer is option 1 i.e. −1.

∠A + ∠B + ∠C = 180°

 { tan$A\over2$ + cosec$B+C\over2$}{tan$A\over2$− cosec $B+C\over2$ }

=  { tan$A\over2$ + cosec$180-A\over2$}{tan$A\over2$− cosec $180-A\over2$ }

=  { tan$A\over2$ + cosec $90-\frac{A}{2}$}{tan$A\over2$− cosec $90-\frac{A}{2}$ }

=  { tan$A\over2$ + sec $A\over2$}{tan$A\over2$− sec $A\over2$}

= { tan²$A\over2$ - sec² $A\over2$}             {sec²a - tan²a = 1}

= -1