Question

If tan a + cot a = 2 find the value of tan^2 a + cot ^2 a

Answer 1

Answer:

2

Step-by-step explanation:

Put a = 45°

since tan 45° = cot 45° = 1

tan² a + cot² a = 1² + 1² = 2

2 is the correct answer.

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Answer 2

Answer:

2

Step By Step Explaination:-

tan a + cot a = 2

Squaring Both the sides we get

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

Therefore:

tan^2 a + cot^2 a + 2×(cot a)×(tan a) = 4

As we Know (cot a) = [1/tan a]

Thus

tan^2 a + cot^2 a + 2×(1/tan a)(tan a) = 4

tan^2 a + cot^2 a + 2 = 4

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

tan^2 a + cot^2 a = 2

Therefore the answer to the question is = 2