TBQ - Prove the following V — task. Maths TNSB Mentoring, Class 10 Crash course.

If

\frac{\sin Y}{1 + \cos Y} = \frac{1}{a}

, then prove that

\frac{a^{2} - 1}{a^{2} + 1} = \cos Y

.

Proof:

\frac{\sin Y}{1 + \cos Y} = \frac{1}{a}

\(a^2 =\)

\(a^2 + 1 =\)

\(a^2 - 1 =\)

LHS \(=\)

\frac{a^{2} - 1}{a^{2} + 1}

\(=\)

\(=\)

\(=\)

\(=\)

\cos Y

\(=\) RHS

Hence, we proved.

Answer variants:

\frac{2 \cos^{2} Y + 2 \cos Y}{\sin^{2} Y}

\frac{1 + \cos^{2} Y + 2 \cos Y}{\sin^{2} Y}

\frac{2 \cos^{2} Y + 2 \cos Y}{2 + 2 \cos Y}

a = \frac{1 + \cos Y}{\sin Y}

\frac{2 + 2 \cos Y}{\sin^{2} Y}

\frac{(\frac{2 \cos^{2} Y + 2 \cos Y}{\sin^{2} Y})}{(\frac{2 + 2 \cos Y}{\sin^{2} Y})}

\frac{2 \cos Y (\cos Y + 1)}{2 (1 + \cos Y)}

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