Answer:
Step-by-step explanation:
Given= 13sina=12
To prove= 1/cos^2a - tan^2a
Proof;
lets take the given equation
13 sin a =12
sin a =12/13
(sin=P/H)
H=13 AND P=12
using Pythagorean theorem
[tex]H^{2}[/tex]=[tex]P^{2}[/tex]+[tex]B^{2}[/tex]
[tex]13^{2}[/tex]=[tex]12^{2}[/tex]+[tex]B^{2}[/tex]
169=144+[tex]B^{2}[/tex]
169-144=[tex]B^{2}[/tex]
25=[tex]B^{2}[/tex]
[tex]\sqrt{25}[/tex]=B
B=5
Using the equation
[tex]\frac{1}{cos^{2}a }[/tex] - [tex]tan^{2} a[/tex]
cos a=[tex]\frac{b}{h}[/tex]= [tex]\frac{5}{13}[/tex]
tan a=[tex]\frac{p}{b}[/tex]=[tex]\frac{12}{5}[/tex]
therefore
[tex]\frac{1}{\frac{5}{13} ^{2} }[/tex] - [tex](\frac{12}{5} )[/tex]²
[tex](\frac{13}{5} )[/tex]² - [tex](\frac{12}{5} )[/tex]²
[tex]\frac{169}{25}[/tex] - [tex](\frac{144}{25} )[/tex]
[tex]\frac{25}{25}[/tex]
1
therefore the answer 1
