Answer:
(a) sec²(θ) -tan²(θ) = 1
Step-by-step explanation:
The identity relation between sec(θ) and tan(θ) is ...
tan²(θ) +1 = sec²(θ)
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When tan²(θ) is subtracted from both sides of this equation, the result matches the first choice:
sec²(θ) -tan²(θ) = 1
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Additional comment
This is a variation of the "Pythagorean" relationship between sine and cosine. There is a similar relation between cot²(θ) and csc²(θ).
[tex]\sin^2\theta+\cos^2\theta=1\\\\\dfrac{\sin^2\theta}{\cos^2\theta}+\dfrac{\cos^2\theta}{\cos^2\theta}=\dfrac{1}{\cos^2\theta}\qquad\text{divide by $\cos^2\theta$}\\\\\tan^2\theta+1=\sec^2\theta[/tex]
