The equivalent expression of the different of two square is -1
Given the following expressions
a cot α = 1
a = 1/cot α = sinα/cosα
b = 1/cos α
We are to find the expression a² - b²
According to difference of two squares;
a² - b² = (a + b) (a - b)
Substitute the given expressions into the formula as shown:
[tex]a^2 - b^2 = (\frac{sin \alpha}{cos \alpha} )^2 - (\frac{1}{cos \alpha} )^2\\a^2 - b^2=\frac{sin^2 \alpha}{cos^2 \alpha} -\frac{1}{cos ^2 \alpha}\\a^2 - b^2=\frac{sin^2 \alpha-1}{cos^2\alpha}\\a^2 - b^2=\frac{-(1-sin^2\alpha)}{cos^2\alpha} \\a^2 - b^2=\frac{-os^2 \alpha}{cos^2 \alpha}\\a^2 - b^2 = -1[/tex]
This shows that the equivalent expression of the difference of two squares is -1
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