Question

CosA=12/13then find cotA+tanA

Answer 1

Answer

± 169/60

$\rule{100}2$

Explanation

Given,

cosA = 12/13

→ secA = 13/12

(since, secA = 1/cosA)

Now, we know that the relation between sec∅ and tan∅ is given by the identity

sec²∅ = 1 + tan²∅

→ sec²A = 1 + tan²A

→ (13/12)² = 1 + tan²A

→ tan²A = 169/144 - 1

→ tan²A = (169 - 144)/144

→ tan²A = 25/144

→ tanA = ± $\sf\frac{5}{12}$

Case - 1

If tanA = 5/12

then, cotA = 12/5

Then, tanA + cotA = 5/12 + 12/5 = 25/60 + 144/60

→ 169/60

Case - 2

If tanA = -5/12

then, cotA = -12/5

then, tanA + cotA = -5/12 - 12/5 = -25/60 - 144/60

→ -169/60