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Chapter 7: Q.21 (page 473)

Establish the identity: $1 + \tan^{2} (- θ) = s e c^{2} (θ)$

Short Answer

Expert verified

We establish the identity $1 + \tan^{2} (- θ) = s e c^{2} (θ)$

Step by step solution

01

Given information

We are given $1 + \tan^{2} (- θ)$

02

tan is an odd function tan(-θ)=-tan(θ)

We get

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

03

Conclusion

We establish the identity $1 + \tan^{2} (- θ) = s e c^{2} (θ)$

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Most popular questions from this chapter

Establish each identity.

$\frac{\sin θ + \cos θ}{\cos θ} - \frac{\sin θ - \cos θ}{\sin θ} = s e c θ c s c θ$

Establish each identity.

$s e c θ - \cos θ = \sin θ \tan θ$

True or False:

$\tan 2 θ + \tan 2 θ = \tan (4 θ)$

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

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

solve each equation on the interval $0 \leq θ < 2 π$

$\sin θ - \sqrt{3} \cos θ = 1$

See all solutions

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