How to prove cos⁡ 20° + cos 100° + cos 140° = 0? скачать в хорошем качестве

How to prove cos⁡ 20° + cos 100° + cos 140° = 0?

Trigonometric Identities Part 2. Start solving the left-hand side members, [cos(20deg)]+[cos(100deg)]+[cos(140deg)], of the given equation until its right-hand side member, 0, is obtained. This equation can be prove by employing the Sum of Functions Formula cosA + cosB = 2{cos[(A+B)/2]}{cos[(A-B)/2]}. Firstly, group the left-hand side members of the given equation this way, {[cos(20deg)]+[cos(100deg)]}+[cos(140deg)], then employ the Sum of Functions Formula only to the terms inside the curly bracket. Evaluate and simplify. The result will be {[2cos(60deg)][cos(-40deg)]}+[cos(140deg)]. Substitute the exact value of cos(60deg) = 1/2, and cos(-40deg) = cos(40deg), since cos(-theta) = cos(theta). Simplify further. After that, the new result will be [cos(40deg)]+[cos(140deg)]. Once again, employ the Sum of Functions Formula. Evaluate and simplify. Mharthy's Channel's Playlists: Differential Calculus    • Prove f'(x) = nx^(n-1), if f(x) = x^n and ...   Complex Numbers    • Prove:⁡⁡  (a⁡+⁡b⁡i)(c⁡+⁡d⁡i)⁡ = ⁡(ac⁡-⁡bd)...   Conversions    • Conversions   Logarithms, etc.    • Logarithms, etc.   Analytic Geometry    • Analytic Geometry   Plane Trigonometry Basics    • Plane Trigonometry Basics   Fractions    • Fractions   Systems of first degree/linear equations    • Systems of first degree/linear equations   Exponents and Radicals    • Exponents and Radicals   Quadratic Equation and Formula, etc.    • Quadratic Equation and Formula, etc.   Division of Polynomials, etc.    • Division of Polynomials, etc.   The Binomial Theorem    • The Binomial Theorem   Trigonometric Formulas    • Trigonometric Formulas   The Exact Values of sin & cos Functions of a Right Triangle    • The Exact Values of sin and cos Functions ...   Trigonometric Identities 1    • Trigonometric Identities 1   Trigonometric Identities 2    • Trigonometric Identities 2   Trigonometric Identities 3    • Trigonometric Identities 3