If x ∈((π/2), π), then ( sec x-1/sec x+1) if equal to

Question

If x ∈((π/2), π), then ( sec x-1/sec x+1) if equal to (A) ( textcosec x + cot x)2 (B) ( sin x - cos x)2 (C) ( textcosec x - cot x)2 (D) ( sec x + tan x)2

Tardigrade Admin · Accepted Answer

Given, x ∈((π/2), π) ∴ ( sec x-1/ sec x+1)=((1/ cos x)-1/(1) cos x+1) = (1- cos x/1+ cos x) × (1- cos x/1- cos x) = (12-2 cos x+ cos 2 x/1- cos 2 x) = (1-2 cos x+ cos 2 x/ sin 2 x) = operatornamecosec2 x-2 cot x operatornamecosec x+ cot 2 x =( operatornamecosec x- cot x)2

Q. If $x \in (\frac{π}{2}, π)$ , then $\frac{sec x - 1}{sec x + 1}$ if equal to

$(cosec x + co t x)^{2}$

$(sin x - cos x)^{2}$

$(cosec x - co t x)^{2}$

$(sec x + t an x)^{2}$

$(sec x - t an x)^{2}$

Q. If x∈(2π​,π), then secx+1secx−1​ if equal to

(cosecx+cotx)2

(sinx−cosx)2

(cosecx−cotx)2

(secx+tanx)2

(secx−tanx)2