Good day.
Here's the problem: "Apply the addition formula for tangent function to show that if 0 < θ < π/2, then cot(π/2 - θ) = sin (θ)"
So, the first part was all right, since I already did a couple of this kind of problems today:
Then there was a point when I got stuck and even the solution I have didn't help. Here it is:
Tip: in the middle you can see that 1 is replace with tan(pi/2)/tan(pi/2) and tan θ is replaced with (tan pi/2 * tan θ) / tan pi/2
I made it to the point where "(1/tan(pi/2) + tan θ) / (1 - (tan θ / tan (pi/2))" and I struggled over an hour to transform it into "tan θ". That's the line right before the answer in the second screenshot. Could you kindly explain how you derive "tan θ" from "(1/tan(pi/2) + tan θ) / (1 - (tan θ / tan (pi/2))"?
Thank you in advance and have a great day!
Here's the problem: "Apply the addition formula for tangent function to show that if 0 < θ < π/2, then cot(π/2 - θ) = sin (θ)"
So, the first part was all right, since I already did a couple of this kind of problems today:
Then there was a point when I got stuck and even the solution I have didn't help. Here it is:
Tip: in the middle you can see that 1 is replace with tan(pi/2)/tan(pi/2) and tan θ is replaced with (tan pi/2 * tan θ) / tan pi/2
I made it to the point where "(1/tan(pi/2) + tan θ) / (1 - (tan θ / tan (pi/2))" and I struggled over an hour to transform it into "tan θ". That's the line right before the answer in the second screenshot. Could you kindly explain how you derive "tan θ" from "(1/tan(pi/2) + tan θ) / (1 - (tan θ / tan (pi/2))"?
Thank you in advance and have a great day!