(sin/cos)/ ( 1/cos - 1) = I'm stumped
(sin/cos)(1-cos)/cos
sin(1 - cos)/cos^2
I see nothing special about this.
could it be:
(sin/cos) [1/(cos-1)] ???
then
(sin/cos) [1/(cos-1)][(cos+1)/cos+1)]
(sin/cos)(cos+1)/(cos^2-1)
-(sin/cos)(cos+1)/sin^2
- (cos+1)/sin cos
The actual question goes :
make the left the same as the right:
left side:
tan/sec - 1 = right side
sin/1-cos
I bet you mean
tan/(sec - 1) = sin/(1-cos)
PARENTHESES ARE VITAL
otherwise you are just wasting time
(sin/cos)/[(1/cos)-cos/cos] = sin/(1-cos)
sin/(1-cos) = sin/(1-cos)
Thanks Damon.
To simplify this expression, let's first simplify each term individually.
1. Simplify (sin/cos):
Recall that sin(x)/cos(x) is equal to tan(x) (tangent function). So, (sin/cos) = tan.
2. Simplify (1/cos - 1):
To simplify this term, we need to rationalize the denominator. Multiply the numerator and denominator by cos to get rid of the fraction:
(1/cos - 1) * (cos/cos) = (cos - cos^2) / cos
Now, simplify the numerator:
1 - cos^2
Recall the identity cos^2(x) + sin^2(x) = 1. Rearranging this, we get:
1 - cos^2(x) = sin^2(x)
Now, we can substitute these simplified expressions back into the original expression:
(sin/cos) / (1/cos - 1) = tan(x) / sin^2(x)
Further simplification is not possible without additional context or values, as this expression is already in its simplest form.