Let α and β be two real roots of the equation k + 1 t a n 2 x - 2 ⋅ λ tan ⁡ x = 1 - k , where k ≠ - 1 and λ are real numbers. If t a n 2 α + β = 50 , then a value of λ is

Question

Let &#945; and &#946; be two real roots of the equation k + 1 t a n 2 x - 2 &#8901; &#955; tan &#8289; x = 1 - k , where k &#8800; - 1 and &#955; are real numbers. If t a n 2 &#945; + &#946; = 50 , then a value of &#955; is

Aicharya · Accepted Answer

k + 1 tan 2 &#8289; x - 2 &#955; tan &#8289; x + k - 1 = 0 tan &#8289; &#945; + tan &#8289; &#946; = 2 &#955; k + 1 t a n &#945; tan &#8289; &#946; = k - 1 k + 1 tan &#8289; &#945; + &#946; = 2 &#955; k + 1 1 - k - 1 k + 1 = 2 &#955; 2 = &#955; 2 tan 2 &#8289; &#945; + &#946; = &#955; 2 2 = 50 &#955; = &#177; 10

Let α and β be two real roots of the equation k + 1 t a n 2 x - 2 ⋅ λ tan ⁡ x = 1…

Solution

Let &#945; and &#946; be two real roots of the equation k + 1 t a n 2 x - 2 &#8901; &#955; tan &#8289; x = 1…

Solution

Let α and β be two real roots of the equation k + 1 t a n 2 x - 2 ⋅ λ tan ⁡ x = 1…