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 Trigonometric Identities (1) Conditional trigonometrical identities We have certain trigonometric identities Like sin2 θ cos2 θ = 1 and 1 tan2 θ = sec2 θ etc Such identities are identities in the sense that they hold for all value of the angles which satisfy the given condition among them and they are calledSinθ 1 2 √ 2 2 √ 3 2 cosθ √ 3 2 √ 2 2 1 2 tanθ √ 3 3 1 √ 3 secθ cscθ tanθ sinθ cosθ 1 cotθ 圖1 三角函數的基本恆等關係圖 ∼順伯的窩∼ 三角學 I 第1頁/共39頁 If 1 sin2θ = 3sinθ cosθ , then prove that tanθ = 1 or ½ Given 1sin 2 θ = 3 sin θ cos θ Dividing LHS and RHS equations with sin 2 θ, We get, cosec 2 θ 1 = 3 cot θ Since, cosec 2 θ – cot 2 θ = 1 ⇒ cosec 2 θ = cot 2 θ 1 ⇒ cot 2 θ 11 = 3 cot θ ⇒ cot 2 θ 2 = 3 cot θ ⇒ cot 2 θ –3 cot θ 2 = 0 Splitting the middle term and then solving the equation, Acceleration Of Gravity Sinθ=1/2 θ=