Question

(cosθ+secθ)= 5/2 then (cos2θ+sec2θ)=

Answer 1

Answer:

Given,

cos θ + sec θ = 5/2

cos θ + (1/cos θ) = 5/2

cos2θ + 1 = (5/2) cos θ

2 cos2θ + 2 = 5 cos θ

2 cos2θ – 5 cos θ + 2 = 0

2 cos2θ – 4 cos θ – cos θ + 2 = 0

2 cos θ(cos θ – 2) – 1(cos θ – 2) = 0

(2 cos θ – 1)(cos θ – 2) = 0

cos θ = 1/2, cos θ = 2

cos θ = 2 is not possible since the range of cos θ is [-1, 1].

Thus, cos θ = 1/2

cos θ = cos π/3

Therefore, θ = 2nπ ± π/3

Step-by-step explanation:

Hope it helps (~‾▿‾)~