Question #297ca

2 Answers
Jul 10, 2017

cottheta

Explanation:

"using the "color(blue)"trigonometric identities"

•color(white)(x)cottheta=costheta/sintheta

•color(white)(x)sectheta=1/costheta

rArrcot^2theta . sintheta .sectheta

=(cos^2theta)/(sin^2theta)xxsinthetaxx1/costheta

=(cancel(costheta)costheta)/(cancel(sintheta)sintheta)xxcancel(sintheta)xx1/cancel(costheta)

=costheta/sintheta

=cottheta

color(red)"OR"

costheta/sintheta=costhetaxx1/sintheta=costhetacsctheta

Jul 10, 2017

cot^2 theta * sintheta * sectheta = cot theta

Explanation:

cot^2 theta * sintheta * sectheta

Rewrite in terms of sin and cos

= (cos^2theta / sin^2theta) * sintheta * (1/costheta)

= frac{costheta * color(red)(costheta) * color(red)(sintheta)}{sintheta * color(red)(sintheta) * color(red)(costheta) }

= cottheta