Prove that each equation is an identity. cos(θ+(π)/(4))+sin(θ-(π)/(4))=0

Name: Problem 56, Chapter 8: Precalculus
Uploaded: 2020-07-26T05:54:23-08:00
Duration: 1 min 4 s
Channel: Subhadeepta Sahoo
Description: Prove that each equation is an identity. cos(θ+(π)/(4))+sin(θ-(π)/(4))=0

step 1 In this question we can write cost theta plus pi by 4 as cost theta cost 5 by 4 minus sine theta

Prove that each equation is an identity....

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Key Concepts

Trigonometric Sum and Difference Formulas

This concept involves the formulas used to expand trigonometric functions of sums or differences of angles. For cosine and sine, these expansions allow one to write functions like cos(? + ?) and sin(? ? ?) in terms of products of sine and cosine of the individual angles. These formulas are foundational in proving trigonometric identities since they enable the decomposition and eventual cancellation of terms.

Standard Trigonometric Values

This refers to the well-known values of trigonometric functions at specific angles, such as the values of sine and cosine at certain standard angles. Knowledge of these values is critical when simplifying expressions after applying sum and difference formulas, as it converts the abstract forms into numerical coefficients, making the cancellation of terms and final reduction more apparent.

Algebraic Simplification in Trigonometric Proofs

Algebraic simplification involves combining like terms and using fundamental algebraic operations to reduce a complex expression into a simpler or more recognizable form. In the context of proving trigonometric identities, after applying formulas such as the sum and difference formulas, careful algebraic manipulation is key to demonstrating that the expression holds for all values, thereby establishing it as an identity.

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