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Ainat [17]
2 years ago
6

If a cot α = 1 and b cos α = 1, find a2 – b 2​

Mathematics
1 answer:
S_A_V [24]2 years ago
4 0

The equivalent expression of the<u> different of two square</u> 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 <u>difference of two squares;</u>

a² - b² =  (a + b) (a - b)

Substitute the given expressions into the formula as shown:

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

This shows that the equivalent expression of the<u> difference of two squares</u> is -1

Learn more here: brainly.com/question/11084694

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