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1/sin 45∘sin ...

Question

$\frac{1}{s i n 45^{\circ} s i n 46^{\circ}} + \frac{1}{s i n 47^{\circ} s i n 48^{\circ}} + \frac{1}{s i n 49^{\circ} s i n 50^{\circ}} + . . . . + \frac{1}{s i n 133^{\circ} s i n 134^{\circ}} = k$ then the value of $k s i n 1^{\circ}$ is___

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Solution

Multiply on both sides by $s i n 1^{\circ}$ and simplify

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1

= 0.017

radians, then the approximate value of

sin 46

\frac{1}{sin 45^{\circ} sin 46^{\circ}} + \frac{1}{sin 47^{\circ} sin 48^{\circ}} + . . . + \frac{1}{sin 135^{\circ} sin 134^{\circ}} = \frac{1}{sin A^{\circ}}

\frac{1}{sin 1^{\circ} sin 2^{\circ}} + \frac{1}{sin 2^{\circ} sin 3^{\circ}} + . . . + \frac{1}{sin 89^{\circ} sin 90^{\circ}} = \frac{B}{sin 1^{\circ}},

then which of the following is/are correct ?

\frac{1}{k} = \frac{1}{3} + \frac{1}{4}

then the value of K is

Q. lf the slope of the line

(\frac{1}{a} + \frac{k}{b}) x + (\frac{1}{b} + \frac{k}{a}) y - (1 + k) = 0

- 1

, then the value of

k

360 \sum k = 1 (\frac{1}{k \sqrt{k + 1} + (k + 1) \sqrt{k}}) = a,

then the value of

19 a

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