Question

If tanθ +cotθ=3, the value of (tan²θ +cot²θ)(tan³θ +cot³θ)

Answer 1

Answer:

(tan²θ +cot²θ)=7

(tan³θ +cot³θ)=18

Step-by-step explanation:

According to the problem ,

tanθ +cotθ=3

now , Squaring on both sides , we get

(tanθ+ cotθ)²= 9

tan²θ+ 2 tanθ cotθ + cot²θ=9

as we know that cot is inverse ratio of tan ...tanθ. cotθ=1

tan²θ+cot²θ +2 = 9

tan² θ  +cot² θ     = 7

∴tan² θ  +cot² θ = 7

now

tanθ +cotθ=3

cubing on both sides,

(tanθ+cotθ)³= 27

tan³ θ  + 3 tan²θ cotθ + 3 tanθ cot²θ  + cot³θ  = 27

tan³θ+ cot³θ + 3 tanθcotθ( tanθ+cotθ)= 27

tan³θ + cot³ θ    + 3(1) (3)=27

tan³θ+cot³θ+9 = 27

tan³θ+cot³θ= 18