Question

If tan A+ 1 /tanA=2. show
tan ²A+1/tan²A=2​

Answer 1

Answer:

(tan a + I / tan a)^2 = tan^2a + 1/tan^2a + 2

(as (a+b)^2 = a^2 + b^2 + 2ab)

2^2 = tan^2a + 1/tan^2a + 2

4 = tan^2a + 1/tan^2a + 2

4-2 = tan^2a + 1/tan^2a

2 = tan^2a + 1/tan^2a

hence proved

Answer 2

Step-by-step explanation:

cotA= 1/tanA

so,

tanA+cotA=2....(1)

at A=45°

it satisfied eqn 1

now ,

=(tan^(45°)+1)/tan^2(45°)

=(1+1)/1^2

=2/1

=2