Use the product-to-sum identities to express $2\cos\left(3x\right)\cos\left(9x\right)$2cos(3x)cos(9x) as a sum or difference of two trigonometric functions.

Easy

2min

Express $\cos\left(3x+2y\right)\cos\left(x-y\right)$cos(3x+2y)cos(x−y) as a sum or difference of two trigonometric functions.

Easy

6min

Evaluate $\cos105^\circ\cos15^\circ$cos105°cos15° by first expressing it as a sum or difference of two trigonometric functions using the product-to-sum identities.

Easy

4min

Express $2\sin\left(3x\right)\sin\left(4x\right)$2sin(3x)sin(4x) as a sum or difference of two trigonometric functions by using the product-to-sum identities.

Easy

1min

Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

Solve equations using trigonometric identities

Interactive practice questions

Outcomes

11.SF.TF.1

What is Mathspace

About Mathspace