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Chapter 7: Q. 110 (page 475)

Make up an identity that is not a Fundamental Identity.

Short Answer

Expert verified

The few make up identites are as follows,

$(\cos e c θ - c o t θ) (\cos e c θ + c o t θ) = 1 (1 - \cos^{2} θ) (1 + c o t^{2} θ) = 1$

Step by step solution

01

Step 1. Given Information

The given information is to make up few identities.

02

Step 2. Explanation

As we know that if an equation is said to be balanced different values of angles then it is treated as an identity.

So, while solving this exercise we have proved a lot many equations which can be treated as identities. For example,

$(\cos e c θ - c o t θ) (\cos e c θ + c o t θ) = 1 (1 - \cos^{2} θ) (1 + c o t^{2} θ) = 1 (9 s e c^{2} θ - 5 \tan^{2} θ) = 5 + 4 s e c^{2} θ$

If we will substitute different values of angles we will see that they will satisfy the equation.

Hence, they are treated as an identity.

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Most popular questions from this chapter

Establish each identity.

$\frac{1 + \sin θ}{1 - \sin θ} = {(s e c θ + \tan θ)}^{2}$

In Problems 9–36, find the exact value of each expression.

$\csc [\cos^{- 1} (- \frac{\sqrt{3}}{2})]$

Rewrite over a common denominator:

$\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)}$

Establish each identity.

$\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$

Multiply: $\frac{\sin (θ)}{1 + \cos (θ)} \frac{1 - \cos (θ)}{1 - \cos (θ)}$

See all solutions

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