Question

(1+cot 0)² + (1-cot0)²= 2cosec²0​

Answer 1

Step-by-step explanation:

Solution :

(1 + cot A)² + (1 – cot)²

opening the brackets using identity

(a + b)² = a² + b² + 2ab.

(a – b)² = a² + b² – 2ab.

☆☞ 1 + cot²A + 2cotA + 1 + cot²A – 2cotA

☆☞ 2cotA – 2cotB = 0

So,

☆☞ 2 + 2cot²A

☆☞ 2(1 + cot²A)

Using identity 1 + cot²A = cosec²A

☆☞ 2cosec²A (LHS)

Hence

• It is proved.

Some Identities

☆☞ 1 + cot²A = cosec²A

☆☞ 1 + Tan²A = sec²A

☆☞ sin²A + cos²A = 1

Answer 2

Step-by-step explanation:

Solution :

(1 + cot A)² + (1 - cot)²

OPENING THE BRACKETS USING IDENTITY

(a + b)² = a² + b² + 2ab.

(a - b)² = a² + b² - 2ab.

1 + cot²A + 2cotA + 1+ cot²A - 2cotA

2cotA - 2cotB = 0

V

So,

✩2 +2cot²A ✩2(1 + cot²A)

Using identity 1 + cot²A = cosec²A

2cosec²A (LHS)

Hence

It is proved.

Some Identities

1+ cot²A = cosec²A

1+ Tan²A = sec²A

sin²A + cos²A = 1

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