Question

If tan theta +cot theta =2, find the value of tan^{​​​​2} theta + cot^{​​​​2} theta

Answer 1

Given, tan theta + cot theta = 2

= tan theta + 1/tan theta = 2

= tan^2 theta + 1/tan theta = 2

= tan^2 theta + 1 = 2 tan theta

= tan^2 theta + 1 - 2 tan theta = 0

= (tan theta - 1)^2 = 0

= tan theta - 1 = 0

= tan theta = 1

theta = 45 degrees

So, tan^2theta + cot^2 theta = (tan 45)^2 + (cot 45)^2

= 1^2 + 1^2

= 2