📏 trigonometry

1. **Énoncé du problème :** Calculer et simplifier l'expression $$C = 3 \cos^2 34^\circ + \cos 60^\circ + 3 \cos^2 56^\circ$$ et simplifier l'expression $$VD = \frac{\cos y}{\sqrt{

1. **Problem Statement:** Find the difference between $\sin 2x$ and $2 \sin x$. 2. **Recall the formula for double angle sine:**

1. نبدأ ببيان المشكلة: نريد معرفة عدد المرات التي تصل فيها الدالة $$d(x) = \sin(x + 1)$$ إلى قيمتها العظمى في الفترة $$[0, 2\pi]$$. 2. الدالة $$\sin(\theta)$$ تصل إلى قيمتها العظمى

1. نبدأ بتحديد المشكلة: نريد معرفة عدد نقاط تقاطع منحني الدالة $d(x) = \cos(2x)$ مع محور السينات في الفترة $[0, 2\pi]$. 2. نقاط تقاطع المنحني مع محور السينات تحدث عندما تكون قيمة ا

1. نبدأ بقراءة السؤال: د(س) = 2 جَأ س + 1 2. د(س) هي دالة جيب تمام مضروبة في 2 ثم أضيف إليها 1.

1. **State the problem:** Find the value of $\sin 135^\circ$. 2. **Recall the formula and rules:** The sine of an angle in degrees can be found using the unit circle or sine additi

1. **State the problem:** Find the values of $\sin 135^\circ$ and $\tan 15^\circ$. 2. **Recall formulas and important rules:**

1. The problem is to evaluate $\cos \frac{2\pi}{3}$.\n\n2. Recall that the cosine function for an angle $\theta$ in radians is the x-coordinate of the point on the unit circle at t

1. Let's start by stating the problem: You want to learn about the inverse trigonometric functions arcsin, arccos, and arctan. 2. These functions are the inverses of the sine, cosi

1. ප්‍රශ්නය: A + B = 45° නම්, (1 + \tan A)(1 + \tan B) = 2 බව සනාථ කරන්න. 2. අපිට දැනගත යුතුයි: \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}.

1. **State the problem:** Solve the equation $$1 + \frac{\sin x}{\cos x} = \frac{\cos x}{1 - \sin x}$$ for $x$. 2. **Rewrite the equation:** Note that $\frac{\sin x}{\cos x} = \tan

1. **State the problem:** Solve the equation $\sin 2x = \sin x$ for $x$.\n\n2. **Recall the formula and rules:** The equation $\sin A = \sin B$ implies that either:\n\n$$A = B + 2k

1. We are given the equation $$2(\sin^6 x + \cos^6 x) - 3(\sin^4 x + \cos^4 x) + 1 = 0$$ and need to solve it. 2. Recall the Pythagorean identity: $$\sin^2 x + \cos^2 x = 1$$.

1. **State the problem:** We need to verify the identity $$\frac{\sin x + \cos x}{\cos^3 x} = 1 + \tan x + \tan^2 x + \tan^3 x$$. 2. **Recall definitions and formulas:**

1. **State the problem:** Prove or verify the identity $$\sin^8 x - \cos^8 x = (\sin^2 x - \cos^2 x)(1 - 2\sin^2 x \cos^2 x)$$. 2. **Recall formulas and rules:**

1. The problem is to find the function and understand the behavior of $\sin x$. 2. The sine function is a fundamental trigonometric function defined as the ratio of the length of t

1. مسئله را بیان می‌کنیم: مقدار عبارت $$A=\frac{\sin(-50^\circ)+\sin(112^\circ)}{\cos(158^\circ)-\tan(22^\circ)}$$ را بیابید. 2. فرمول‌ها و قوانین مهم:

1. The problem is to understand how the expression $\pi - \pi \sin^2 x$ can be transformed into $\pi \sin^2 x$. 2. Start with the original expression:

1. **Problem (a): Solve $\cos 2x + \cos x = 0$.** Use the double-angle formula: $\cos 2x = 2\cos^2 x - 1$.

1. Muammo: $4\cos^3 x + 3\sin x = 3\cos x + 4\sin^3 x$ tenglamaning $[0;2\pi]$ oraliqdagi eng katta va eng kichik ildizlari yig'indisini topish va $[-\pi;0]$ oraliqda nechta ildizg

1. مسئله: در مثلث قائم‌الزاویه ABC با زاویه Ă قائمه و ضلع AC برابر ۴، اگر \( \tan \alpha = \frac{3}{4} \) باشد، مقدار سینوس زاویه \( \theta \) را بیابید. 2. فرمول‌ها و نکات مهم: