Question

$(1 - \cos^{2}a)cossec \: a = 1$
plzzz give me a answer​

Answer 1

$\Large{\underline{\underline{\red{\mathfrak{Correct \: Question :}}}}}$

${\rm{Prove\: that \: (1 \: - \: {\cos}^{2}A) \cosec A\: = \: 1}}$

$\Large{\underline{\underline{\red{\mathfrak{Solution :}}}}}$

Take $\mathbb{L.H.S,}$

⇒(1 - Cos²A)CosecA

As we know ,

$\Large{\underline{\boxed{\sf{1 \: - \: \cos ^2 A \: = \: \sin ^2 A}}}}$

So,

⇒Sin²A(Cosec²A)

Also,

$\Large{\underline{\boxed{\sf{\cosec ^2 A \: = \: \frac{1}{\sin ^2 A}}}}}$

So,

⇒Sin²A(1/Sin²A)

⇒Sin²A/Sin²A

Now,

$\mathbb{L.H.S \: = \: R.H.S}$

$\LARGE {\boxed{\boxed{\sf{1 \: = \: 1}}}}$

Hence Proved

____________________________

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Answer 2

$\huge{\orange{\underline{\red{\mathscr{ANSWER:-}}}}}$

Given : (1- Cos²A) Cosec² A = 1

L.H.S : (1- Cos² A) Cosec² A

= Sin² A Cosec² A

[By using the identity , 1- Cos² A = sin²A]

= (Sin A Cosec A)²

= [Sin A x (1/Sin A)]²

[By using the identity , Cosec A = 1/Sin A]

= (1)²

= 1

(1- Cos²A) Cosec² A = 1

L.H.S = R.H.S

Hence Proved..

$\huge{\orange{\underline{\red{\mathscr{THANKS.}}}}}$