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prove the identity, if root 3 cot² theta -4cot theta + root 3 =0, then find the value of cot²theta +tan²theta

Posted by Ravneet Randhawa 4 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Aman Singh 4 years, 5 months ago

Good

0Thank You

Rohan Kumar 4 years, 5 months ago

Given that:- 3cot²θ - 4cotθ +√3=0 To find:- Cot²θ+ tan²θ=? Now, (√3cotθ)² -4cotθ+√3=0 =(√3cotθ)² -3cotθ-1cotθ+√3=0 =√3cotθ(cotθ-√3) -1(cotθ-√3)=0 =(√3cotθ-1)(cotθ-√3)=0 =√3cotθ-1=0 OR =cotθ-√3=0 Cotθ =1/√3 .....(i) OR cot=√3 .....(ii) Now, By equation (i), when cot θ=1/√3 Cot²θ+tan²θ = [(1/√3)²+(√3)²] =[1/3+3] =10/3 _______(iii) By equation (ii), When cotθ=√3 Cot²θ+tan²θ =[(√3)²+(1/√3)²] =[3+1/3] =10/3 ________(iv) Hence, in both cases value of {Cot²θ+tan²θ} is same that is 10/3.

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