Trigonometric Functions and Identities

The video tutorial explores the trigonometric identity of cosine of alpha plus beta. It begins by setting up the problem using geometric lines and then breaks down the expression into simpler parts. The tutorial applies trigonometric ratios to solve the identity, concluding with the result that cosine of alpha plus beta equals the product of the cosines minus the product of the sines of the angles. The proof is similar to the sine identity proof and highlights the differences between the two.

What is the main goal of the video tutorial?

• To explain the Pythagorean theorem

• To solve a quadratic equation

• To derive the cosine of alpha plus beta identity

• To derive the sine of alpha plus beta identity

In the geometric setup, what does the line AC represent?

• The hypotenuse of the triangle

• The opposite side of the angle

• The base of the triangle

• The adjacent side of the angle

How is the line segment AC expressed in terms of other line segments?

• AF plus DE

• AF times DE

• AF minus DE

• DE minus AF

What is the purpose of expressing AF over AE in the algebraic manipulation?

• To find the cotangent of alpha

• To find the tangent of alpha

• To find the cosine of alpha

• To find the sine of alpha

What is the relationship between angle DBE and angle alpha?

• Angle DBE is equal to alpha

• Angle DBE is supplementary to alpha

• Angle DBE is complementary to alpha

• Angle DBE is twice alpha

What trigonometric function is represented by DE over BE?

• Tangent of alpha

• Cotangent of alpha

• Sine of alpha

• Cosine of alpha

What is the final expression for cosine of alpha plus beta?

• cos(alpha) * cos(beta) + sin(alpha) * sin(beta)

• sin(alpha) * cos(beta) + cos(alpha) * sin(beta)

• cos(alpha) * cos(beta) - sin(alpha) * sin(beta)

• sin(alpha) * cos(beta) - cos(alpha) * sin(beta)

Which trigonometric identity is similar in derivation to the cosine of alpha plus beta?

• Cotangent of alpha plus beta

• Secant of alpha plus beta

• Tangent of alpha plus beta

• Sine of alpha plus beta

What is the significance of the angle 90 minus alpha in the derivation?

• It is used to find the sine of beta

• It is used to find the cosine of beta

• It is used to find the tangent of beta

• It is used to find the cotangent of beta

What is the final step in the derivation of the cosine of alpha plus beta identity?

• Dividing the cosine of both angles

• Subtracting the sine of both angles

• Multiplying the cosine of both angles

• Adding the sine of both angles