If π θ 3 π 2 and cos ⁡ θ = - 3 5 , then t a n θ 4 is equal to

Question

If π θ 3 π 2 and cos ⁡ θ = - 3 5 , then t a n θ 4 is equal to, 5 - 1 2, 5 + 1 2, - 5 + 1 4, - 5 - 1 4

MARKS App · Accepted Answer

cos ⁡ θ = - 3 5 ⇒ 2 c o s 2 θ 2 - 1 = - 3 5 2 c o s 2 θ 2 = 1 - 3 5 = 2 5 c o s θ 2 = ± 1 5 ⇒ c o s θ 2 = - 1 5 ∵ π 2 θ 2 3 π 4 Now, t a n 2 θ 4 = 1 - c o s θ 2 1 + c o s θ 2 = 1 + 1 5 1 - 1 5 = 5 + 1 5 - 1 t a n 2 θ 4 = 5 + 1 2 4 = 5 + 1 2 2 ⇒ t a n θ 4 = 5 + 1 2 ∵ π 4 θ 4 3 π 8

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