If tanA + cotA = 2, then what is the value of tan2
A + cot2
A.
Answers
Given :-
• tan A + cot A = 2
We have to find the value of tan² A + cot² A
So, We have,
⇒ tan A + cot A = 2
The expression which we have to find the value of has tan and cot squared. So, Let's square both sides of the given equation.
⇒ (tan A + cot A)² = 2²
⇒ tan² A + cot² A + 2tanAcotA = 4
[ ∵ (a + b)² = a² + b² + 2ab ]
⇒ tan² A + cot² A + 2 tan A × 1/tan A = 4
[ ∴ cot A = 1 / tan A ]
⇒ tan² A + cot² A + 2 = 4
⇒ tan² A + cot² A = 2
So, Our answer would be 2.
Some Important Formulae :-
• 1 + tan² A = sec² A
• 1 + cot² A = cosec² A
• sin² θ + cos² θ = 1
• tan θ = sinθ / cosθ
Answer:
✪ Given :-
- tanA + cotA = 2
✪ To Find :-
- What is the value of tan²A + cot²A
✪ Solution :-
➙ tanA + cotA = 2
➣ By squaring both sides we get,
⇒ (tanA + cotA)² = (2)²
⇒ tan²A + cot²A + 2tanAcotA = 4
⇒ tan²A + cot²A + 2 = 4
⇒ tan²A + cot²A = 4 - 2
➠ tan²A + cot²A = 2
The value of tan²A + cot²A =