Trigonometric Simplification Using Double Angle Identities

The video tutorial explains how to simplify a trigonometric expression using a double angle identity. It begins by identifying the relevant identity for the product of sine and cosine, specifically the double angle identity for sine. The tutorial then demonstrates solving the equation and performing substitutions to simplify the expression. The final result is a single trigonometric expression, expressed as the sine of 144 degrees divided by four.

What is the initial expression given in the problem that needs simplification?

• sine 72 degrees times cosine 90 degrees

• cosine 72 degrees times cosine 72 degrees

• sine 72 degrees times sine 72 degrees

• cosine 72 degrees times sine 72 degrees

Which double angle identity is relevant for simplifying the given expression?

• cotangent double angle identity

• sine double angle identity

• cosine double angle identity

• tangent double angle identity

What is the formula for the sine double angle identity?

• sine 2a = 2 sine a cosine a

• sine 2a = sine^2 a + cosine^2 a

• cosine 2a = cosine^2 a - sine^2 a

• tangent 2a = 2 tangent a / (1 - tangent^2 a)

What substitution is performed for cosine 72 degrees times sine 72 degrees?

• one half sine 144 degrees

• one fourth cosine 144 degrees

• one half cosine 144 degrees

• one fourth sine 144 degrees

What is the result of dividing both sides of the identity by two?

• cosine a times sine a = sine 2a

• cosine a times sine a = one half sine 2a

• cosine a times sine a = one fourth sine 2a

• cosine a times sine a = sine a

What is the simplified expression after performing the substitution?

• one half sine 144 degrees

• one half cosine 144 degrees

• one fourth cosine 144 degrees

• one fourth sine 144 degrees

What is the final simplified form of the expression?

• cosine 144 degrees divided by two

• sine 144 degrees divided by two

• cosine 144 degrees divided by four

• sine 144 degrees divided by four

What is the angle used in the final trigonometric expression?

• 144 degrees

• 180 degrees

• 72 degrees

• 90 degrees

What is the coefficient of the sine function in the final expression?

• one fifth

• one third

• one fourth

• one half

What is the purpose of using a double angle identity in this problem?

• To simplify the expression to a single trigonometric function

• To find the exact value of the expression

• To solve a quadratic equation

• To convert the expression into a polynomial