📏 trigonometry

1. সমীকরণ: $\sec 5x = \csc 10x$ সমাধান করব। 2. $\sec 5x = \frac{1}{\cos 5x}$ এবং $\csc 10x = \frac{1}{\sin 10x}$ তাই সমীকরণ হবে:

1. The problem states that we want to find $h$ given the equation $\cos(60) = \frac{1}{h}$. 2. Recall that $\cos(60^\circ) = \frac{1}{2}$.

1. **State the problem:** We have points O, A, and B with distances OA = 20 km, OB = unknown, and AB = 50 km. Bearings from O to A is 334° and from O to B is 54°. We want to find t

1. **State the problem:** We have two yachts starting from point O. Yacht A sails 20 km at a bearing of 334° from O. Yacht B sails such that point B is 50 km from A, and the bearin

1. **State the problem:** We have points O, A, and B with distances OA = 20 km and OB unknown, but AB = 50 km. Bearings from O are 334° to A and 54° to B. We want the bearing of A

1. **State the problem:** Given the equation $7\cos\theta - \sin\theta = 5$ and the condition $\tan\theta > 0$, find $\tan\theta$. 2. **Rewrite the equation:** We want to express t

1. **State the problem:** Given the equation $7\cos\theta - \sin\theta = 5$ and the condition $\tan\theta > 0$, find $\tan\theta$. 2. **Rewrite the equation:** We have

1. **Stating the problem:** Given that $A + B = \frac{\pi}{4}$, we want to simplify the expression $\frac{\cos B - \sin B}{\cos B + \sin B}$. 2. **Rewrite the expression:** The exp

1. The problem is to find an expression for $\tan 4\theta$ in terms of $\tan \theta$. 2. Use the double-angle formula for tangent:

1. **State the problem:** Solve the equation $$\sec 2\theta - 2 \tan 2\theta + 2 \tan \theta = 0$$ for $$0 < \theta < 360$$ degrees. 2. **Rewrite in terms of sine and cosine:** Rec

1. **State the problem:** Prove that $$\sec^2\theta - 2\tan^2\theta + 2\tan\theta = 0$$ and find the values of $$\theta$$. 2. **Recall identities:** We know that $$\sec^2\theta = 1

1. The problem is to solve the equation $$0 = -4\sin(x) - 4\cos(2x)$$ for $x$. 2. Start by rewriting the equation:

1. **State the problem:** We are given a triangle with points A, B, and C. We know |AB| = 8 km, |BC| = 13 km, and the bearing of B from C is 230°. We need to find: (a) the distance

1. **Problem statement:** An aircraft flies from A to B, distance AB = 600 km. Due to bad weather, it detours via C. The line CA makes an angle of 28° 15' with AB, and CA = 500 km.

1. The term "basic angle" typically refers to the smallest positive angle between the terminal side of a given angle and the x-axis in standard position. 2. It is often used in tri

1. The problem is to find the value of $\sin 10^\circ$. 2. Since $10^\circ$ is not one of the standard angles with simple sine values, we can use the sine addition formula or appro

1. Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles, especially right triangles. 2. The primary functions in trigo

1. مسئله را بیان می‌کنیم: معادله $$\sin^{140^\circ}(a) + \cos^{140^\circ 5}(a) + \sin^{140^\circ 6}(a) = \frac{1}{3702}$$ را در بازه $$a \in \left[ \frac{\pi}{4} , \frac{3\pi}{4} \

1. **State the problem:** We have a camera positioned $x$ feet horizontally from the base of a missile launching pad. A missile of length $a$ feet is launched vertically. The base

1. **Giải phương trình a):** Bài toán: Giải phương trình $$\frac{2\cos 2x - 8 \cos x + 7}{\cos x} = 1$$.

1. **Prove** $ (\sin \theta + \cos \theta)^2 + (\sin \theta - \cos \theta)^2 = 2 $. Step 1: Expand each square: