PYQ - Prove the following identity I — task. Maths TNSB Mentoring, Class 10 Crash course.

Check the following identity.

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

Proof:

Answer variants:

\(sin^{2} A\)

\(cosec A\)

\(cos^{2} A\)

\(cot A\)

\begin{array}{l} LHS = \frac{\sin A}{1 + \cos A} \\ = \frac{\sin A}{1 + \cos A} \times \frac{1 - \cos A}{1 - \cos A} \\ = \frac{\sin A (1 - \cos A)}{1 - \cos^{2} A} \\ = \frac{\sin A (1 - \cos A)}{i} \\ = \frac{1 - \cos A}{\sin A} \\ = \frac{1}{\sin A} - \frac{\cos A}{\sin A} \\ = i - i \\ = RHS \end{array}

Did you find an error?

3. PYQ - Prove the following identity I