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Home Question Bank Math Trigonometry Archive 2025 January 01

Trigonometry Questions from Jan 01,2025

Browse the Trigonometry Q&A Archive for Jan 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( \sec ^{6} \theta-\tan ^{6} \theta=1+3 \tan ^{2} \theta \cdot \sec ^{2} \) soln, 26. \( x \) को मान पत्ता लगाउनुहोस् (Solve for \( x \) ): \( 3 \sin 420^{\circ}+x \cos 120^{\circ} \cdot \tan 225^{\circ}=x \cot 120^{\circ} \). Ans: \( x=-9 \) 5. प्रमाणित गर्नुहोस् (Prove that): \( \frac{\tan A-\sec A+1}{\tan A+\sec A-1}=\frac{\cos A}{1+\sin A} \) \( \sin 15+i \cos 15)^{2} \) equals to: \( \frac{\sqrt{3}+i}{2} \) \( \frac{1+\sqrt{3} i}{2} \) \( \left. \begin{array} { l } { \frac { \sin 210 ^ { \circ } \cos 300 ^ { \circ } \tan 240 ^ { \circ } } { \cos 120 ^ { \circ } \tan 150 ^ { \circ } \sin 330 ^ { \circ } } } \\ { [ \sin ( - \theta ) + \cos ( 360 - \theta ) ] [ \cos ( 90 - \theta ) + \frac { \sin \theta } { \tan \theta } ] } \end{array} \right. \) \( 0 / 1^{\star} \quad \begin{array}{l}\text { The general solution of the } \\ \text { equation : } \operatorname{Tan}(\Theta+20)=\operatorname{Cot}(3 \Theta \\ +30)\end{array} \) EXERCICE3: (5 points) 1. Résous dams R, requation \( 2 t^{2}+\sqrt{3} t-3=0 \) 2. Détermine les nombres réels \( A \) et \( B \) tels que pourt tout \( x \in \mathbb{R} \), on ait: \[ \sqrt{3} \cos x+\sin x=A \sin (x+B) \] 3. a. Utilise les résultats des questions 1. et 2. pour résoudre dans l'intervalle ] \( -\pi \); \( \pi \) ] léquation \( (E)=\left(2 \cos ^{2} x+\sqrt{3} \cos x-3\right)(\sqrt{3} \cos x+\sin x-\sqrt{3})=0 \) 4. Reprisente les images des solutions de (E) sur un cercle trigonométrique. 1. Résous dans R, réquation \( 2 t^{2}+\sqrt{3} t-3=0 \) 2. Détermine les nombres réels \( A \) et \( B \) tels que pourt tout \( x \in \mathbb{R} \), on ait: \( \sqrt{3} \cos x+\sin x=A \sin (x+B) \) 3. a Utilise les résultats des questions 1 . ct 2 . pour résoudre dans l'intervalle \( 1-\pi ; \pi \) ] l'équation \( (E) \) : \( \left(2 \cos ^{2} x+\sqrt{3} \cos x-3\right)(\sqrt{3} \cos x+\sin x-\sqrt{3})=0 \) 4. Représente les images des solutions de(E) sur un cercle trigonométrique. \( \tan x \) 3. Soit un angle aigu \( \alpha \) vériliant: \( \sin \alpha+\cos \alpha=\frac{1}{2} \) Calcule : \( \sin \alpha \times \cos \alpha ; \sin ^{3} \alpha+\cos ^{3} \alpha \) et \( \sin ^{4} \alpha+\cos ^{4} \alpha \) 12. Giver that \( \cos A=5 / \) and angle \( A \) is acute, Jin the value of 2 Tan \( A+3 \) sin \( A \)
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