Question

If tanA=√3, verify that 1+cot²A=cosec²A

Answer 1

Given, tanA = √3

we know, tan60° = √3

so, tanA = tan60°

therefore, A = 60°

now, LHS = 1 + cot²A

put A = 60° , then 1 + cot²A = 1 + cot²60°

= 1 + {1/√3}² = 1 + 1/3

= 4/3

and RHS = cosec²A = cosec²60°

= {2/√3}² = 4/3

here it is clear that LHS = RHS

hence, verified.