Respuesta :
[tex]\bf sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
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sin^2(\theta)\cdot sec^2(\theta)\implies sin^2(\theta)\cdot \cfrac{1^2}{cos^2(\theta)}\implies \cfrac{sin^2(\theta)}{cos^2(\theta)}\iff tan^2(\theta)[/tex]
The equation tan² θ = sin² θ × sec² θ is an identity of the trigonometry. Then the correct option is C.
What is trigonometry?
Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
A. cot θ + tan θ = 1
[tex]\rm cot\theta+tan\theta =1\\\\\dfrac{cos \theta}{sin \theta} + \dfrac{sin\theta}{cos\theta} = 1\\\\\\\dfrac{cos^2\theta + sin^2\theta}{sin \theta cos \theta} = 1\\\\\\sin \theta \ cos \theta = 1[/tex]
B. sec² θ+cosec² θ = 1
[tex]\rm sec\theta+cosec\theta =1\\\\\dfrac{1}{sin^2 \theta} + \dfrac{1}{cos^2\theta} = 1\\\\\\\dfrac{cos^2\theta + sin^2\theta}{sin^2 \theta cos^2 \theta} = 1\\\\\\sin^2 \theta \ \ cos^2 \theta = 1[/tex]
C. tan² θ = sin² θ × sec² θ
[tex]\rm sin^2\theta * sec ^2 \theta =tan^2 \theta\\\\\dfrac{sin^2}{cos^2 \theta} = tan^2 \theta \\\\tan^2 \theta = tan^2 \theta[/tex]
D. cos² θ = sec² θ × tan² θ
[tex]\rm sec^2\theta * tan^2 \theta =cos^2 \theta\\\\\dfrac{sin^2}{cos^2 \theta} * \dfrac{1}{cos^2 \theta} = cos^2 \theta \\\\sin^2 \theta = cos^6 \theta[/tex]
The equation tan² θ = sin² θ × sec² θ is an identity of the trigonometry.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
