Trigonometric Identities and Formulas

The video tutorial explains the derivation of formulas for tangent of x+y and x-y using known properties of sine and cosine. It begins by assuming familiarity with basic trigonometric identities and then derives the tangent formulas by expressing them in terms of sine and cosine. The tutorial also covers the properties of negative angles and how they relate to tangent calculations.

What is the formula for sine of x plus y?

• sine x cosine y + cosine x sine y

• sine x sine y + cosine x cosine y

• cosine x cosine y - sine x sine y

• sine x cosine y - cosine x sine y

Which of the following is the correct expression for cosine of x plus y?

• cosine x cosine y + sine x sine y

• sine x sine y - cosine x cosine y

• cosine x cosine y - sine x sine y

• cosine x sine y + sine x cosine y

How is tangent of x plus y defined in terms of sine and cosine?

• cosine of x minus y over sine of x minus y

• sine of x plus y over cosine of x plus y

• sine of x minus y over cosine of x minus y

• cosine of x plus y over sine of x plus y

What operation is performed on both the numerator and denominator to express tangent in terms of tangents of x and y?

• Add cosine of x cosine of y

• Divide by cosine of x cosine of y

• Subtract sine of x sine of y

• Multiply by sine of x sine of y

What does the expression 'sine of x over cosine of x' simplify to?

• Tangent of y

• Tangent of x

• Sine of y

• Cosine of x

What is the simplified form of the tangent of x plus y?

• Tangent of x plus tangent of y over 1 minus tangent of x times tangent of y

• Tangent of x minus tangent of y over 1 minus tangent of x times tangent of y

• Tangent of x plus tangent of y over 1 plus tangent of x times tangent of y

• Tangent of x minus tangent of y over 1 plus tangent of x times tangent of y

How is tangent of negative x expressed?

• Tangent of x

• Negative tangent of x

• Sine of x over negative cosine of x

• Negative sine of x over cosine of x

What is the formula for tangent of x minus y?

• Tangent of x plus tangent of y over 1 minus tangent of x times tangent of y

• Tangent of x plus tangent of y over 1 plus tangent of x times tangent of y

• Tangent of x minus tangent of y over 1 plus tangent of x times tangent of y

• Tangent of x minus tangent of y over 1 minus tangent of x times tangent of y

What is the relationship between tangent of negative y and tangent of y?

• Tangent of negative y is the same as tangent of y

• Tangent of negative y is the negative of tangent of y

• Tangent of negative y is the reciprocal of tangent of y

• Tangent of negative y is the square of tangent of y

How can tangent of x minus y be rewritten using the tangent addition formula?

• Tangent of x plus negative y

• Tangent of x minus y

• Tangent of x minus negative y

• Tangent of x plus y