Question #297ca

2 Answers
Jim G.
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#

Anjali G
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#

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