Question

If tan theta =4/3, find the value of sin theta+cos theta/sin theta-cos theta. PROPER ANSWER= BRAINLIEST

Answer 1

Step-by-step explanation:

tan theta=4/5= P/B

By using Pythagorous theorem

Hypotenuse=5

sin theta= 4/5 and cos theta=3/5

Therefore, (4/5 + 3/5) / (4/5-3/5)

=7/5 / 1/5

=7

Answer 2

Solution :

Attachment a diagram of right angled triangle according to the question.

$\underline{\bf{Given\::}}}$

tan Ф = 4/3

$\underline{\bf{Explanation\::}}}$

As we know that;

$\boxed{\bf{tan\:\theta = \dfrac{Perpendicular}{Base} }}}$

$\mapsto\sf{tan\:\theta =\dfrac{BC}{AC} =\dfrac{4}{3} }$

$\underline{\boldsymbol{By\:using\:Pythagoras\:theorem\::}}}$

$\mapsto\sf{(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2} }\\\\\mapsto\sf{(AB)^{2} = (AC)^{2} + (BC)^{2} }\\\\\mapsto\sf{(AB)^{2} = (3)^{2} + (4)^{2} }\\\\\mapsto\sf{(AB)^{2} = 9+16}\\\\\mapsto\sf{(AB)^{2} = 25}\\\\\mapsto\sf{AB = \sqrt{25} }\\\\\mapsto\bf{AB = 5\:unit}$

Now;

$\mapsto\sf{\dfrac{sin\theta+cos\theta }{sin \theta-cos \theta} }\\\\\\\mapsto \sf{\frac{\dfrac{Perpendicular }{Hypotenuse } + \dfrac{Base }{Hypotenuse } }{\dfrac{Perpendicular }{Hypotenuse } -\dfrac{Base }{Hypotenuse } } }\\\\\\\mapsto\sf{\dfrac{\dfrac{BC}{AB} + \dfrac{AC}{AB} }{\dfrac{BC}{AB} - \dfrac{AC}{AB} } }\\\\\\\mapsto\sf{\dfrac{\dfrac{4}{5} + \dfrac{3}{5} }{\dfrac{4}{5} - \dfrac{3}{5} } }\\\\\\\mapsto\sf{\dfrac{\dfrac{4+3}{5} }{\dfrac{4-3}{5} }}$

$\mapsto\sf{\dfrac{\dfrac{7}{5} }{\dfrac{1}{5} } }\\\\\\\mapsto\sf{\dfrac{7}{\cancel{5}} \times \dfrac{\cancel{5}}{1}} \\\\\\\mapsto\sf{\dfrac{7}{1} }\\\\\\\mapsto\bf{7}$

Thus,

The value of sinФ + cosФ / sinФ - cosФ will be 7 .