Question

ig tanA+ cot A=3 , find the value of tan^2+cot^2A



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Answer 1

Given:

• tanA + cotA = 3

To find:

• tan²A + cot²A = ?

Solution:

We are given the Relation between tan A and cot A that:

tan A + cot A = 3

Squaring on both sides,

(tan A + cot A)² = 3²

Split using (a + b)² = a² + b² + 2ab

tan²A + cot²A + 2 tanAcotA = 9

tanAcotA can be written as 1 since they are reciprocals to each other.

⇒ tan²A + cot²A + 2(1) = 9

⇒ tan²A + cot²A + 2 = 9

⇒ tan²A + cot²A = 9 - 2

⇒ tan²A + cot²A = 7

∴ tan²A + cot²A = 7

KNOW MORE:

• sin and cosec are reciprocals to each other.
• cos and sec are reciprocals to each other.