Question

If tan θ = 7/24 then evaluate (Sin θ + Cos ) sec θ

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \tan \theta = \frac{7}{24} }$

TO DETERMINE

The value of

$\displaystyle \sf{ ( \sin \theta + \cos \theta ) \sec \theta }$

EVALUATION

Here it is given that

$\displaystyle \sf{ \tan \theta = \frac{7}{24} }$

Now

$\displaystyle \sf{ ( \sin \theta + \cos \theta ) \sec \theta }$

$\displaystyle \sf{ = \sin \theta \times \sec \theta + \cos \theta \times \sec \theta }$

$\displaystyle \sf{ = \sin \theta \times \frac{1}{ \cos \theta} + \cos \theta \times \frac{1}{ \cos \theta} }$

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

$\displaystyle \sf{ = \tan \theta + 1 }$

$\displaystyle \sf{ = \frac{7}{24} + 1 }$

$\displaystyle \sf{ = \frac{7 + 24}{24} }$

$\displaystyle \sf{ = \frac{31}{24} }$

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