Question

sin A + cos A / sin A - cosA = 7/3, find tan A? a.5/3 b.3/5 c.2/5 d.5/2​

Answer 1

Solution:

Given –

$\tt \longrightarrow \dfrac{ \sin(x) + \cos(x) }{ \sin(x) - \cos(x) } = \dfrac{7}{3}$

• We have to find out tan(x).

On cross multiplying, we get,

$\tt \longrightarrow 3(\sin(x) + \cos(x)) = 7(\sin(x) - \cos(x) )$

$\tt \longrightarrow 3\sin(x) + 3\cos(x) = 7\sin(x) - 7\cos(x)$

$\tt \longrightarrow 3\cos(x) + 7 \cos(x) = 7\sin(x) -3 \sin(x)$

$\tt \longrightarrow 10 \cos(x) = 4\sin(x)$

Dividing both sides by cos(x), we get,

$\tt \longrightarrow 10 = 4 \times \dfrac{ \sin(x) }{ \cos(x) }$

We know that,

$\tt\longrightarrow\dfrac{ \sin(x) }{ \cos(x) } = \tan(x)$

So,

$\tt \longrightarrow 4 \tan(x) = 10$

$\tt \longrightarrow\tan(x) = \dfrac{10}{4}$

$\tt \longrightarrow\tan(x) = \dfrac{5}{2}$

• So, the value of tan(x) is 5/2.

Answer:

• tan(x) = 2½.

Learn More:

1. Relationship between sides.

• sin(x) = Height/Hypotenuse.
• cos(x) = Base/Hypotenuse.
• tan(x) = Height/Base.
• cot(x) = Base/Height.
• sec(x) = Hypotenuse/Base.
• cosec(x) = Hypotenuse/Height.

2. Square formulae.

• sin²x + cos²x = 1.
• cosec²x - cot²x = 1.
• sec²x - tan²x = 1

3. Reciprocal Relationship.

• sin(x) = 1/cosec(x).
• cos(x) = 1/sec(x).
• tan(x) = 1/cot(x).

4. Cofunction identities.

• sin(90° - x) = cos(x) and vice versa.
• cosec(90° - x) = sec(x) and vice versa.
• tan(90° - x) = cot(x) and vice versa.