Consider the following statements : 1. If θ/1-θ + θ/1+θ = 4 , where 0 2. If 3 tan θ + cot θ = 5 cosec θ, where 0 Which of the statements given above is/are correct ?

CDS 2018 PYQ with Answer — Consider the following statements : 1. If θ/1-θ + θ/1+θ = 4 , where 0…

2018 · Q65

Consider the following statements :

1If θ/1-θ + θ/1+θ = 4 , where 0
2If 3 tan θ + cot θ = 5 cosec θ, where 0 Which of the statements given above is/are correct ?

Elementary MathematicsTrigonometry

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Explanation

Statement 1: cos(theta)/(1 - sin(theta)) + cos(theta)/(1 + sin(theta)) = 2 cos(theta)/(1 - sin^2(theta)) = 2/cos(theta) = 4, so cos(theta) = 1/2 and theta = 60 degrees (theta acute): true. Statement 2: 3 tan(theta) + cot(theta) = 5 cosec(theta) becomes 3 sin^2(theta) + cos^2(theta) = 5 cos(theta), i.e. 2 cos^2(theta) + 5 cos(theta) - 3 = 0, giving cos(theta) = 1/2 (rejecting -3), so theta = 60 degrees: true. Both statements are correct. Hence option C.