Question

find the value of { ( tan - theta ) / sin (540° + theta)}​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{ \tan( - \theta)}{ \sin ( {540}^{ \circ} + \theta) } }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ \frac{ \tan( - \theta)}{ \sin ( {540}^{ \circ} + \theta) } }$

Now

$\displaystyle \sf{ \tan \theta \: \: is \: an \: odd \: function \: of \: \: \theta}$

$\displaystyle \sf{ \therefore \: \tan ( - \theta) = - \tan \theta }$

Again

$\displaystyle \sf{ \sin ( {540}^{ \circ} + \theta)}$

$\displaystyle \sf{ = \sin ( 6 \times {90}^{ \circ} + \theta)}$

$\displaystyle \sf{ = - \sin \theta}$

Hence

$\displaystyle \sf{ \frac{ \tan( - \theta)}{ \sin ( {540}^{ \circ} + \theta) } }$

$\displaystyle \sf{ = \frac{ - \tan \theta}{ - \sin \theta } }$

$\displaystyle \sf{ = \frac{ \tan \theta}{ \sin \theta } }$

$\displaystyle \sf{ = \frac{ \frac{ \sin \theta}{ \cos \theta} }{ \sin \theta } }$

$\displaystyle \sf{ = \frac{1}{ \cos \theta} }$

$\displaystyle \sf{ = { \sec \theta} }$

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Answer 2

Step-by-step explanation:

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