Mathematics: Find the product. Simplify 1/10 times 3/4 A 15/2 B 2/15 C 3/40 D 40/3

ProvedStep-by-step explanation:RequiredShow that:So, we have:So, we have:Rearrange the numeratorSo, we haveSo, we have:Factorize:Rewrite as:...

Find the product. Simplify 1/10 times 3/4 A 15/2 - id1103415210546694, christopherluckey7

annakoslovsky3040

09.03.2021

Proved

Step-by-step explanation:

Required

Show that:

$\frac{1+cos2a+sin2a}{1-cos2a+sin2a}=cota$

cos2a = cos(a + a) = cos^2a - sin^2a

So, we have:

$\frac{1+cos^2a - sin^2a+sin2a}{1-(cos^2a - sin^2a)+sin2a}=cota$

$\frac{1+cos^2a - sin^2a+sin2a}{1-cos^2a + sin^2a+sin2a}=cota$

1- cos^2a = sin^2a

So, we have:

$\frac{1+cos^2a - sin^2a+sin2a}{ sin^2a+ sin^2a+sin2a}=cota$

$\frac{1+cos^2a - sin^2a+sin2a}{2sin^2a+sin2a}=cota$

Rearrange the numerator

$\frac{1 - sin^2a+cos^2a+sin2a}{2sin^2a+sin2a}=cota$

1- sin^2a= cos^2a

So, we have

$\frac{cos^2a+cos^2a+sin2a}{2sin^2a+sin2a}=cota$

$\frac{2cos^2a+sin2a}{2sin^2a+sin2a}=cota$

$sin2a = 2sina\ cosa$

So, we have:

$\frac{2cos^2a+2sinacosa}{2sin^2a+2sinacosa}=cota$

Factorize:

$\frac{cosa(2cosa+2sina)}{sina(2sina+2cosa)}=cota$

Rewrite as:

$\frac{cosa(2cosa+2sina)}{sina(2cosa+2sina)}=cota$

$\frac{cosa}{sina} = cota$

cota = cota

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