Question

If tan A + cotA=2, then what
is the
value of tan²A +cot ²A?

Answer 1

Answer:

2 is the answer

Step-by-step explanation:

tan A + cot A=2

squaring on both the sides,we get

(tan A + cot A)^2 = 4

=> tan²A +cot ²A + 2 tanA cotA = 4

=> tan²A +cot ²A +2 *1 = 4

=> tan²A +cot ²A = 4-2 = 2 ( tan A cotA =1 )

HOPE IT HELPS.

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Answer 2

Given,

tan A + cot A = 2

By squaring both the side

( tan A + cot A = 2 )^2 = (2)^2

tan ^2 A + cot ^2 A + 2tanA cot A = 4

tan ^2 A + cot^2 A + 2 = 4. ( tan × cot = 1 )

tan^2 A + cot ^2 A = 4 - 2

tan^2A + cot ^2A = 2

therefore tan^2A + cot^2A = 2