Question

If sin + cosec = 2, find the value of sin^2 + cosec^2 .​

Answer 1

Question:-

$\rm \: if \: \sin( \theta) + \csc( \theta ) = 2$

$\rm \: find \: the \: value \: of \: \sin {}^{2} ( \theta) \: + \csc( \theta)$

Solution:-

Take

$\rm \: \sin( \theta) + \csc( \theta ) = 2$

Now squaring on both side , we get

$\rm \: \{\sin( \theta) + \csc( \theta ) \} {}^{2} =( 2) {}^{2}$

By using this identity

$\rm(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab$

We get

$\rm \: \sin {}^{2} ( \theta) + \csc {}^{2} ( \theta) + 2 \times \sin( \theta) \times \csc( \theta) = 4$

Trigonometry identities

$\rm \csc( \theta) = \frac{1}{ \sin( \theta) }$

We get

$\rm \: \sin {}^{2} ( \theta) + \csc {}^{2} ( \theta) + 2 \times \sin( \theta) \times \frac{1}{ \sin( \theta) } = 4$

$\rm \: \sin {}^{2} ( \theta) + \csc {}^{2} ( \theta) + 2 = 4$

$\rm \: \sin {}^{2} ( \theta) + \csc {}^{2} ( \theta) = 4 - 2$

$\rm \: \sin {}^{2} ( \theta) + \csc {}^{2} ( \theta) = 2$

Answer:-

$\rm \: \sin {}^{2} ( \theta) + \csc {}^{2} ( \theta) = 2$

Answer 2

sin^2 + cosec^2 . is 2

hope it helps u

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