Question

please solve with steps

Answer 1

Sin(65°) = Sin(90° - 25°)

As Sin(90° - θ) = Cos(θ)

⇒ Sin(65°) = Cos(25°)

⇒ Sin²(65°) = Cos²(25°)

As Sin²(θ) + Cos²(θ) = 1

⇒ Sin²(25°) + Sin²(65°) = Sin²(25°) + Cos²(25°) = 1

Tan(5°) = Tan(90° - 85°)

As Tan(90° - θ) = Cot(θ)

⇒ Tan(5°) = Cot(85°)

Tan(15°) = Tan(90° - 75°)

⇒ Tan(15°) = Cot(75°)

As Tanθ × Cotθ = 1

⇒ Tan(5°) × Tan(85°) = Cot(85°) × Tan(85°) = 1

⇒ Tan(15°) × Tan(75°) = Cot(75°) × Tan(75°) = 1

As Tan(30°) = 1/√3

Substituting all the Values :

The Value of Question = 1 + √3(1/√3) = 1 + 1 = 2