Let z1= sec (5 π/3)+i operatornamecosec (3 π/4) and z2= tan (4 π/3)+i cot (5 π/4) are two complex numbers Statement-1: z1 z2 Statement-2: sec (5 π/3) tan (4 π/3) and operatornamecosec (3 π/4) cot (5 π/4)

Question

Let z1= sec (5 π/3)+i operatornamecosec (3 π/4) and z2= tan (4 π/3)+i cot (5 π/4) are two complex numbers Statement-1: z1 >z2 Statement-2: sec (5 π/3) > tan (4 π/3) and operatornamecosec (3 π/4) > cot (5 π/4) (A) Statement- 1 is true, statement- 2 is true and statement- 2 is correct explanation for statement- 1 . (B) Statement- 1 is true, statement- 2 is true and statement- 2 is NOT the correct explanation for statement- 1 . (C) Statement- 1 is true, statement- 2 is false. (D) Statement- 1 is false, statement- 2 is true.

Tardigrade Admin · Accepted Answer

Correct answer is (d) Statement- 1 is false, statement- 2 is true.

Q. Let z1​=sec35π​+icosec43π​ and z2​=tan34π​+icot45π​ are two complex numbers Statement-1: z1​>z2​ Statement-2: sec35π​>tan34π​ and cosec43π​>cot45π​

Statement- 1 is true, statement- 2 is true and statement- 2 is correct explanation for statement- 1 .

Statement- 1 is true, statement- 2 is true and statement- 2 is NOT the correct explanation for statement- 1 .

Statement- 1 is true, statement- 2 is false.

Statement- 1 is false, statement- 2 is true.

Correct answer is (d) Statement- 1 is false, statement- 2 is true.

Q. Let $z_{1} = sec \frac{5 π}{3} + i cosec \frac{3 π}{4}$ and $z_{2} = tan \frac{4 π}{3} + i cot \frac{5 π}{4}$ are two complex numbers
Statement-1: $z_{1} > z_{2}$
Statement-2: $sec \frac{5 π}{3} > tan \frac{4 π}{3}$ and $cosec \frac{3 π}{4} > cot \frac{5 π}{4}$