If sin ⁡ x + cos ⁡ x = 7 2 , where x ∈ 0 , π 4 , then the value of t a n x 2 is equal to

Question

If sin ⁡ x + cos ⁡ x = 7 2 , where x ∈ 0 , π 4 , then the value of t a n x 2 is equal to, 3 - 7 3, 7 - 2 3, 4 - 7 4, 5 - 3 2

MARKS App · Accepted Answer

sin ⁡ x + cos ⁡ x = 7 2 ⇒ 2 t a n x 2 1 + t a n 2 x 2 + 1 - t a n 2 x 2 1 + t a n 2 x 2 = 7 2 ⇒ 4 t a n x 2 + 2 - 2 t a n 2 x 2 = 7 + 7 t a n 2 x 2 ⇒ 2 + 7 t a n 2 x 2 - 4 t a n x 2 + 7 - 2 = 0 ⇒ t a n x 2 = 4 ± 16 - 4 2 + 7 7 - 2 2 2 + 7 = 4 ± 16 - 4 × 3 2 2 + 7 tan x 2 = 2 ± 1 2 + 7 = 1 2 + 7 or 3 2 + 7 t a n x 2 = 7 - 2 3 or 7 - 2 But, as x 2 ∈ 0 , π 8 ⇒ t a n x 2 = 7 - 2 3

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