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Chapter 7: Q. 28 (page 485)

In problem 23-32,find the exact value of the each expression

tan40掳-tan10掳1+tan40掳tan10掳

Short Answer

Expert verified

The exact value of thetan40掳-tan10掳1+tan40掳tan10掳=13

Step by step solution

01

Step 1.Given information

The given expressiontan40掳-tan10掳1+tan40掳tan10掳

02

Step 2.Finding exact value of the given expression

We will use the formula tan伪-尾=tan伪-tan尾1+tan伪tan尾

The indicated expression is in the form of the right side of the formula

tan伪-尾=tan伪-tan尾1+tan伪tan尾

where 伪=40掳and尾=10掳

Therefore we get

role="math" localid="1646551449161" tan40掳-tan10掳1+tan40掳tan10掳=tan(40掳-10掳)=tan(30掳)=13

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