## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 49

#### Answer

In standard trigonometry texts, only sine, cosine and tangent of the sum or difference of 2 numbers or values are necessary, as the rest can be deduced using Reciprocal Identities.

#### Work Step by Step

Remember from Reciprocal Identities: $$\cot\theta=\frac{1}{\tan\theta}\hspace{1.5cm}\csc\theta=\frac{1}{\sin\theta}\hspace{1.5cm}\sec\theta=\frac{1}{\cos\theta}$$ So as we see here, we can always derive the cotangent, cosecant and secant if we already know the tangent, sine and cosine of the sum or difference of 2 numbers or angles. Therefore, in standard trigonometry texts, only sine, cosine and tangent of the sum or difference are necessary, as the rest can be deduced using Reciprocal Identities.

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