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Evaluation of a Determinant

Cot^-1[√1-sin...

Question

Cot^-1[√1-sinx+√1+sinx/√1-sinx -√1+sinx] is equal to (where x belongs to (0 to 90))

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y = {cot}^{- 1} [\begin{matrix} \frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}} \end{matrix}]

0 < x < \frac{π}{2}

\frac{d y}{d x}

\frac{sin x}{1 + sec x} + \frac{sin x}{sec x - 1} = 2

0^{\circ} < x < 90^{\circ}

then cosec x has the value equal to

S h o w t h a t

c o t^{- 1} (\frac{\sqrt{1 + s i n x} + \sqrt{1 - s i n x}}{\sqrt{1 + s i n x} - \sqrt{1 - s i n x}}) = \frac{x}{2}

f o r x \in (0, \frac{π}{2})

x

I I^{n d}

\frac{\sqrt{1 + sin x} + \sqrt{1 - sin x}}{\sqrt{1 + sin x} - \sqrt{1 - sin x}}

Q. The value of

{cot}^{- 1} {\frac{\sqrt{1 - sin x} + \sqrt{1 + sin x}}{\sqrt{1 - sin x} - \sqrt{1 + sin x}}}

(0 < x < \frac{π}{2})

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Evaluation of a Determinant

Standard XII Mathematics

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