Question

if sin(90-A)= 1/2 then find the value of tan A + cot A​

Answer 1

Step-by-step explanation:

sin(90-A)= cot A

Therefore, cot A = 1/2

cot 60= 1/2

Therefore , A= 60

Now,

tan A+ cot A= tan 60 + cot 60

= √3 + 1/√3

= 3+1/√3

= 4/√3

= 4√3 / 3

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Answer 2

Answer:

The value of tan A + cot A​ = 4/$\sqrt{3}$

Step-by-step explanation:

Given : Sin (90-A) = 1/2

            tan A + Cot A = ?

Solution : Sin(90-A) = Cos A = 1/2 ---------1

                Sin²A+Cos²A = 1

                Sin²A = 1- Cos²A -----------2

            Substituting 1 in 2, we get

               Sin²A = 1- 1/2 x 1/2

                         = 1 - 1/4

                          = 3/4

          ∴ SinA = $\sqrt{3}$/2 --------------3

tanA + CotA = SinA/CosA + CosA/SinA ----------------4

Substituting 1 & 3 in 4, we get

tanA + cotA =  $\sqrt{3}$/2/1/2 + 1/2/ $\sqrt{3}$/2

                     = $\sqrt{3}$ + 1/$\sqrt{3}$  

                    = (3+1)/$\sqrt{3}$

                    = 4/$\sqrt{3}$