Math, asked by balaji9980, 6 months ago

If tanA + cotA = 2, then what is the value of tan2

A + cot2

A.​

Answers

Answered by DrNykterstein
25

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

Answered by BrainlyHero420
142

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

\therefore The value of tan²A + cot²A = \boxed{\bold{\large{2}}}

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