Question

☺ Please answer with proper solution.

Answer 1

the given equation is possible only when P = 45°

as tan 45 = cot 45 = 1
so answer will remain 2 irrespective of the Power n.
A is correct answer

Answer 2

Given Equation is tanP + cotP = 2.

$tan P + \frac{1}{tan P} = 2$

$\frac{tan P * tan P + 1}{tan P} = 2$

$\frac{tan^2 P + 1}{tan P} = 2$

$tan^2 P + 1 = 2tan P$

tan ^2P - 2tanP + 1 = 0

(tan P - 1)^2 = 0

tan P - 1 = 0

tan P = 1

tan P = tan 45

P = 45  ---------- (1) 


Now,

Tan^ P + cot^ P = tan^n(P) + cot^n(P)

                          = (tanP)^n + (cotP)^n

                          = (1)^n + (1)^n

We know that 1^n = 1.

So,

1 + 1

2.


Therefore the answer is the option (A) - 2.

Hope this helps!