Question

tan theta + cot theta = 1, then find the value of tan square theta + cot square theta

Answer 1

HERE IS YOUR ANSWER :-

Tan A + cot A = 2

=> tan A + (1/tanA) = 2

=> (tan^2 A + 1)/tan A = 2

=> tan^2 A + 1= 2tan A

=> tan^2 A - 2tan A + 1 = 0

=> (tan A - 1)^2 = 0

=> tanA-1=0 =>. tan A = 1

So tan^2 A + cot ^2

A= 1+1 = 2

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Answer 2

tanΦ + cot Φ = 1

Squaring both sides
(tan Φ + cot Φ)² = (1)²
tan²Φ + cot²Φ + 2×tanΦ×cot Φ = 1
tan²Φ + cot²Φ +2 =1. (tanΦ .cotΦ = 1)
tan²Φ + cot²Φ = -1