Question

Using the figure below, write 5 trigonometric statements. Be sure to include the postulates definitions, or theorems that justify your statements.

Answer 1

$In \: \triangle EDF , \angle D = 90\degree$

$DF = 9 , DE = 40 \: and \: EF = 41$

$i) Sin^{2} E + Cos^{E}$

$= \Big( \frac{9}{41}\Big)^{2} + \Big( \frac{40}{41}\Big)^{2}$

$= \frac{81}{1681} + \frac{1600}{1681}$

$= \frac{81+1600}{1681}$

$= \frac{1681}{1681}$

$= 1$

$\blue { \therefore Sin^{2} E + Cos^{E} = 1 }$

Similarly , we can proof following Trigonometric Identities :

$ii) sec^{2} E - tan^{2} E = 1$

$iii) Cosec^{2} E - Cot^{2} E = 1$

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