Shortcut Trick Convert obtuse angles to supplementary forms: 133° = 180° − 47° and 136° = 180° − 44°. Using 2^(nd) quadrant rules: sec(180° − θ) = −sec θ and cosec(180° − θ) = cosec θ. Expression = cos 47° × (−sec 47°) + sin 44° × cosec 44°. Since cos θ × sec θ = 1 and sin θ × cosec θ = 1: Result = −1 + 1 = 0. ∴ The correct answer is 0. Alternate Method Given: Expression = cos 47° sec 133° + sin 44° cosec 136° Formula Used: sec(180° − θ) = −sec θ cosec(180° − θ) = cosec θ cos θ × sec θ = 1 sin θ × cosec θ = 1 Calculations: ⇒ Split the obtuse angles into (180° − θ) form to simplify. ⇒ sec 133° = sec(180° − 47°) = −sec 47° ⇒ cosec 136° = cosec(180° − 44°) = cosec 44° ⇒ Substitute these simplified values back into the given expression. ⇒ Expression = cos 47° × (−sec 47°) + sin 44° × cosec 44° ⇒ Expression = −(cos 47° × sec 47°) + (sin 44° × cosec 44°) ⇒ Since a trigonometric function multiplied by its reciprocal is exactly 1: ⇒ Expression = −1 + 1 = 0 ∴ The correct answer is 0. Related Concepts: ASTC Rule In the 2^(nd) quadrant (90° to 180°), only Sine (sin) and Cosecant (cosec) are positive. Cosine (cos), Secant (sec), Tangent (tan), and Cotangent (cot) are negative. Reciprocal Identities sin θ × cosec θ = 1 | cos θ × sec θ = 1 | tan θ × cot θ = 1. Supplementary Angles Angles that add up to 180° are supplementary. sin(180° − θ) = sin θ, while cos(180° − θ) = −cos θ.