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Simplify (1/sin)/sin + (cos/sin)/cos
- Thread starter Ramster12
- Start date
D
Deleted member 4993
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csc(x)/sin(x)+cot(x)/cos(x)
Write csc(x) and cot(x) in terms sin(x) and/or cos(x) and continue.... Please share your work with us .
If you are stuck at the beginning tell us and we'll start with the definitions.
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LoyalKnight
New member
- Joined
- Nov 14, 2013
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- 7
Simplify (1/sin)/sin + (cos/sin)/cos
well first (cos/sin)/cos = cos/sin * 1/cos so we get 1/sin
Then we simplify 1/sin * 1/sin = 1/ sin^2
1/sin^2 + 1/sin
= 1/sin^2 + sin/sin^2
= sin +1 /(sin^2)
well first (cos/sin)/cos = cos/sin * 1/cos so we get 1/sin
Then we simplify 1/sin * 1/sin = 1/ sin^2
1/sin^2 + 1/sin
= 1/sin^2 + sin/sin^2
= sin +1 /(sin^2)
D
Deleted member 4993
Guest
Simplify (1/sin)/sin + (cos/sin)/cos
well first (cos/sin)/cos = cos/sin * 1/cos so we get 1/sin
Then we simplify 1/sin * 1/sin = 1/ sin^2
1/sin^2 + 1/sin
= 1/sin^2 + sin/sin^2
= sin +1 /(sin^2)
Always write sin(x), cos(x), tan(x),.... etc. Never write without the arguments such as x or Θ or Ω etc.
Apply grouping symbols to indicate order of operation.
csc(x)/sin(x)+cot(x)/cos(x)
\(\displaystyle \displaystyle{\left [\frac{\frac{1}{sin(x)}}{sin(x)}\right ] + \left [ \frac{\frac{cos(x)}{sin(x)}}{cos(x)}\right ]}\)
\(\displaystyle = \ \displaystyle{\left [\frac{1}{sin^2(x)}\right ] + \left [ \frac{1}{sin(x)}\right ]}\)
\(\displaystyle = \ \displaystyle{\frac{1 \ + \ sin(x)}{sin^2(x)}}\)