Question

cot^2A-1/sin^2A is equal to:

Answer 1

AnsWer :

( D ) - 1.

QuestioN :

$\tt Cot^2 A - \dfrac{1}{Sin^2A} \: is \: Equal \: to \: :$

• ( A ) tan²A.
• ( B ) 1.
• ( C ) cot²A.
• ( D ) - 1.

SolutioN :

$\tt Cot^2 A - \dfrac{1}{Sin^2A} \: is \: Equal \: to \: :$

We know,

• 1 + cot² A = Cosec² A.
• 1 / Sin² A = Cosec² A.

$\tt : \implies Cot^2 A - \dfrac{1}{Sin^2A}$

$\tt : \implies Cot^2 A - Cosec^2A$

$\tt : \implies Cot^2 A - Cosec^2A$

✎ Now, Putting the Cot²A = Cosec²A - 1.

$\tt : \implies \cancel {Cosec^2 A }- 1 - \cancel{Cosec^2A}$

$\tt : \implies - 1.$

♢ Therefore, required value is - 1.

Answer 2

Solution :-

Cot²A - 1 / Sin²A = ?

(A) Tan²A

(B) 1

(C)Cot²A

(D) -1

Explanation :-

=>Cot²A - 1 / Sin²A

=>Cot²A - Cosec²A ---( °.° 1/sin²A = cosec²A)

•As we know that,

Cot²A = Cosec²A - 1

=> .°. Cosec²A -1 - Cosec²A

=> -1 .

.°. Cot²A - 1/Sin²A = -1 .

Hence, the required value is -1.