Prove the identity- 1-cosec A- A-1-sin A-1-sin A-1-cosec A- A-4 MARKS-

Formula: 2 Marks Proof: 2 Marks 1/cosec A cot A 1/sin A=1/sin A=1/cosec A+cot A Grouping similar terms, we get ⇒1/cosec A cot A+1/cosec A+cot A=1/sin A+1/sin A ...

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Standard XII

Chemistry

Introduction to Haloalkanes

Prove the ide...

Question

Prove the identity: $\frac{1}{c o s e c A - c o t A} - \frac{1}{s i n A} = \frac{1}{s i n A} = \frac{1}{c o s e c A + c o t A}$ [4 MARKS]

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Solution

Formula: 2 Marks
Proof: 2 Marks

$\frac{1}{c o s e c A - c o t A} - \frac{1}{s i n A} = \frac{1}{s i n A} = \frac{1}{c o s e c A + c o t A}$
Grouping similar terms, we get
$\Rightarrow \frac{1}{c o s e c A - c o t A} + \frac{1}{c o s e c A + c o t A} = \frac{1}{s i n A} + \frac{1}{s i n A} \Rightarrow \frac{2 c o s e c A}{c o s e c^{2} A - c o t^{2} A} = \frac{2}{s i n A} \Rightarrow 2 c o s e c A = 2 c o s e c A$
which is true
${∵ c o s e c^{2} A - c o t^{2} A = 1}$

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Similar questions

Q. Prove that

\frac{cos A + sin A - 1}{cos A - sin A + 1} = \frac{1}{cosec A + cot A}

, using the identity

{cosec}^{2} A - {cot}^{2} A = 1.

Q. Prove that

\frac{1}{c o s e c A - cot A} - \frac{1}{sin A} = \frac{1}{sin A} - \frac{1}{c o s e c A + cot A}

Q. Prove the following statements.

\frac{1}{c o s e c A - cot A} - \frac{1}{sin A} = \frac{1}{sin A} - \frac{1}{c o s e c A + cot A}

Q. Prove :

\frac{cot A + cosec A - 1}{cot A - cosec A + 1} = \frac{1 + cos A}{sin A}

Prove:

\frac{c o t A + c o s e c A - 1}{c o t A - c o s e c A + 1} = \frac{1 + c o s A}{s i n A} = c o s e c θ + c o t θ = \frac{s i n A}{1 - c o s A}

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Prove the identity: 1cosec A−cot A−1sin A=1sin A=1cosec A+cot A [4 MARKS]

Formula: 2 Marks Proof: 2 Marks 1cosec A−cot A−1sin A=1sin A=1cosec A+cot A Grouping similar terms, we get ⇒1cosec A−cot A+1cosec A+cot A=1sin A+1sin A⇒2cosec Acosec2 A−cot2 A=2sin A⇒2 cosec A=2 cosec A which is true {∵ cosec2 A−cot2 A=1}

Prove the identity: $\frac{1}{c o s e c A - c o t A} - \frac{1}{s i n A} = \frac{1}{s i n A} = \frac{1}{c o s e c A + c o t A}$ [4 MARKS]