Question

Which statement is true for all real values of theta?

Answer 1

(a) sec²(θ) -tan²(θ) = 1

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).

`\sin^2\theta+\cos^2\theta=1\\\\(\sin^2\theta)/(\cos^2\theta)+(\cos^2\theta)/(\cos^2\theta)=(1)/(\cos^2\theta)\qquad\text{divide by $\cos^2\theta$}\\\\\tan^2\theta+1=\sec^2\theta`