177/MR00. problem / Math - Solved Math Problems

MR-177. problem

Source: MathReference: Generic Math Textbook - 177.)

Algebra → Exponential equations and inequalities → Exponential equations

\frac{1 + c t g 2 x \cdot c t g x}{t g x + c t g x}

\frac{1 + c t g 2 x \cdot c t g x}{t g x + c t g x}

= \frac{1 + \frac{c o s 2 x}{s i n 2 x} \cdot \frac{c o s x}{s i n x}}{\frac{s i n x}{c o s x} + \frac{c o s x}{s i n x}}

= \frac{\frac{s i n 2 x \cdot s i n x + c o s 2 x \cdot c o s x}{s i n 2 x \cdot s i n x}}{\frac{s i n^{2} x + c o s^{2} x}{s i n x \cdot c o s x}}

= \frac{\frac{c o s (2 x - x)}{s i n 2 x \cdot s i n x}}{\frac{1}{s i n x \cdot c o s x}}

= \frac{\frac{c o s x}{s i n 2 x \cdot s i n x}}{\frac{1}{s i n x \cdot c o s x}}

= \frac{s i n x \cdot c o s^{2} x}{s i n 2 x \cdot s i n x}

= \frac{s i n x \cdot c o s^{2} x}{2 s i n x \cdot c o s x \cdot s i n x}

= \frac{s i n x \cdot c o s^{2} x}{2 s i n x \cdot c o s x \cdot s i n x}

= \frac{c o s x}{2 s i n x}

= \frac{1}{\frac{2 c o s x}{s i n x}}

= \frac{1}{2 c t g x}

s i n 2 α = 2 \cdot s i n α \cdot c o s α

s i n 2 α = 2 \cdot s i n α \cdot c o s α

s i n 2 α = 2 \cdot s i n α \cdot c o s α

\frac{1 + c t g 2 x \cdot c t g x}{t g x + c t g x} = \frac{1}{2 \cdot c t g x}