Respuesta :

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{1-cos^2(\theta )}{sin^2(\theta )}\implies \cfrac{sin^2(\theta )}{sin^2(\theta )}\implies 1[/tex]

The simplified form of given expression is 1.

Given that:

To simplify: [tex]\dfrac{1-cos^2\theta}{sin^2\theta}[/tex]

Simplification:

The most important and most basic trigonometric identity is:

[tex]sin^2\theta + cos^2\theta = 1[/tex]

Thus, from that identity, we have:

[tex]sin^2\theta + cos^2\theta = 1\\sin^2\theta = 1 - cos^2 \theta[/tex]

Putting that value in given equation:

[tex]\dfrac{1-cos^2\theta}{sin^2\theta} = \dfrac{sin^2\theta}{sin^2\theta} = 1[/tex]

Thus, the simplified form of given expression evaluates to 1.

Learn more about trigonometric identities:

https://brainly.com/question/11049559

Otras preguntas