Question

If tan²a-5tana+1=0 find the value of tan²a+ cot ²a

Answer 1

Given: It is given that tan²A - 5tanA + 1 = 0

To find: The value of tan²A + cot²A

Solution:

It is given that tan²A - 5tanA +1 = 0 , then

tan²A - 5tanA = -1

tanA ( tanA - 5 ) = -1

tanA - 5 = - 1/tanA

tanA - 5 = - cotA

tanA + cotA = 5

Squaring on both the sides, we have

( tanA + cotA )² = 25

tan²A + cot²A + 2tanA cotA = 25

Now, because tanAcotA=1 , therefore the equation becomes,

tan²A + cot²A + 2 = 25

tan²A + cot²A = 23

thus the value of tan²A + cot²A is 23

Answer 2

Answer: 23

Step-by-step explanation:

Given,

tan²A - 5tanA + 1 = 0

tan²A - 5tanA = -1

tanA(tanA - 5) = -1

tanA - 5 = -1/tanA

We know that 1/tanA = cotA

So,

tanA - 5 = -cotA

tanA + cotA = 5

Now, Making square of both sides,

(tanA +cotA)² = 5²

Expanding RHS by (a + b)² = a² + b² +2ab

tan²A + cot²A + 2tanA.cotA = 25

tan²A + cot²A + 2tanA ×(1/tanA) = 25

tan²A + cot²A + 2 = 25

tan²A + cot²A = 25 - 2

tan²A + cot²A = 23