The equations of three lines are given below.

Mathematics

1 answer:

Anton [14]2 years ago

7 0

Answer:

Step-by-step explanation:

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Can anyone help me solve a trigonomic identity problem and also help me how to do it step by step?

dusya [7]

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad csc(\theta)=\cfrac{1}{sin(\theta)}
\\\\\\
sin^2(\theta)+cos^2(\theta)=1\\\\
-------------------------------\\\\$

$\bf \cfrac{cos(\theta )cot(\theta )}{1-sin(\theta )}-1=csc(\theta )\\\\
-------------------------------\\\\
\cfrac{cos(\theta )\cdot \frac{cos(\theta )}{sin(\theta )}}{1-sin(\theta )}-1\implies \cfrac{\frac{cos^2(\theta )}{sin(\theta )}}{\frac{1-sin(\theta )}{1}}-1\implies 
\cfrac{cos^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{1-sin(\theta )}-1
\\\\\\
\cfrac{cos^2(\theta )}{sin(\theta )[1-sin(\theta )]}-1\implies 
\cfrac{cos^2(\theta )-1[sin(\theta )[1-sin(\theta )]]}{sin(\theta )[1-sin(\theta )]}$

$\bf \cfrac{cos^2(\theta )-1[sin(\theta )-sin^2(\theta )]}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{cos^2(\theta )-sin(\theta )+sin^2(\theta )}{sin(\theta )[1-sin(\theta )]}
\\\\\\
\cfrac{cos^2(\theta )+sin^2(\theta )-sin(\theta )}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{\underline{1-sin(\theta )}}{sin(\theta )\underline{[1-sin(\theta )]}}
\\\\\\
\cfrac{1}{sin(\theta )}\implies csc(\theta )$

7 0

3 years ago

10. Make q the subject of the formula 5(q + p) = 4 + 8p

vichka [17]

The formula subject to q is $\frac{4+3p}{5}$