Question

ii) (cos²A - 1) (cot² A + 1) = -1​

Answer 1

Answer:

sin²A+cos²A= 1 and 1+cot²A= cosec ²A

Step-by-step explanation:

now , -sin²A =cos²A-1

and , cot²A+1=cosec²A

putting the value we get

-sin²A*cosec²A

-1/cosec²A*cosec²A

-1

hence proved

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Answer 2

Solution :-

We need to prove that

(cos²A - 1)(cot²A + 1) = - 1

Taking LHS

As we know that

➥ 1 + cot²A = cosec²A

Substituting

➛ (cos²A - 1) × cosec²A

Using identity

➥ (a - b) × c = ab - bc

Similarly

➛ cos²A × cosec²A - cosec²A

Substituting

➥ cosecA = 1/sinA

➛ cos²A × 1/sin²A - cosec²A

➛ cos²A/sin²A - cosec²A

As we know that

➥ cosA/sinA = cotA

Similarly

➛ cot²A - cosec²A

➛ - (cosec²A - cot²A)

We have the expression in the form of the 3rd trigonometric identity

➥ cosec²θ - cot²θ = 1

➛ - 1

Now , comparing with RHS

➨ LHS = RHS

Hence , proved !