Question

tan²theta + cot²theta=2
find the value of theta

no useless answer​

Answer 1

so theta equals to Forty five degree

Answer 2

Given :-

• tan²θ + cot²θ = 2

To find :-

• Value of θ

Solution :-

→     tan²θ + cot²θ = 2

→      tan²θ + cot²θ = 2 ( 1 )

∵ tan θ cot θ = 1

therefore,

→      tan²θ + cot²θ = 2 tan θ cot θ

→      tan²θ + cot²θ - 2 tan θ cot θ = 0

using algebraic identity

( a - b )² = a² + b² - 2 ab

→      ( tan θ - cot θ )² = 0

→      tan θ - cot θ = 0

→      tan θ = cot θ

so,

∵  tan θ = cot θ

it means  θ = 45°

Hence,

→     θ = 45°     ( Ans. )