Question

if tanA-cotA=4,then what is the value of tanA+cotA

Answer 1

Given that,
tanA - cotA = 4
Now, squaring on both sides we have,
(tanA - cotA)² = 4²

tan²A + cot²A - 2tanAcotA = 16

tan²A + cot²A - 2 = 16

tan²A + cot²A = 18

(tanA + cotA)² - 2tanAcotA = 18

(tanA + cotA)² - 2 = 18

(tanA + cotA)² = 20

tanA + cotA = √20

tanA + cotA = 2√5


Hence value of,
tanA + cotA = 2√5