Step-by-step explanation:
From Trig
1 + tan²x = Sec²x
Also
Sec²x = 1/cos²x
Now
Cot²x = 1/tan²x = cos²x/sin²x
Putting all together
Cot²x(1+tan²x)
= Cot²x(sec²x)
= cos²x/sin²x(1/cos²x)
cos²x on the numerator and that one the denominator cancels out
we have
= 1/sin²x
From Trig
1/sin²x = cosec²x
So Our Answer = cosec²x.
Given:
<span>tan(B/2) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Apply the half angle formula to convert tan(B/2) to terms of B: </span>
<span>sin(B) / (1+cos(B)) = sec(B) / (sec(B) * csc(B) + csc(B)) </span>
<span>Convert everything else to be in terms of sin and cos: </span>
<span>sin(B) / (1+cos(B) = (1/cos(B)) / ((1/cos(B)) * (1/sin(B)) + (1/sin(B))) </span>
<span>Multiply right side by "sin(B)/sin(B)" to simplify the fractions: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + 1) </span>
<span>Change "1" to cos(B)/cos(B) and then combine over </span>
<span>common denominator: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1/cos(B)) + cos(B)/cos(B)) </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) / ((1+cos(B))/cos(B)) </span>
<span>Dividing by a fraction equals multiplying by its reciprocal: </span>
<span>sin(B) / (1+cos(B) = (sin(B)/cos(B)) * (cos(B) / (1+cos(B))) </span>
<span>Multiply terms on the right side (canceling cos(B) terms): </span>
<span>sin(B) / (1+cos(B) = sin(B) / (1+cos(B)) </span>
Answer:
Slope is 3/-7
Step-by-step explanation:
Try this solution:dy/dx=y⁴cosx; y⁻⁴dy=cosxdx;
