Question

Date
Page

lf 16 cot x = 12, then sin x- cos x /
sin x + cos x is equal ? ​

Answer 1

Answer:

⇢ $\sf{\dfrac{1}{7}}$

Step-by-step explanation:

As we know,

ㅤㅤㅤㅤㅤㅤ16 cot x = 12

⇢ cot x = 12/16

ㅤ

Now simplify 12/16, we get:

⇢ 1/6 = 3/4

ㅤ

The the value of cot x is also equal to (3/4).

ㅤ

here,

• 3 = Base,
• 4 = Perpendicular.

ㅤ

Using Pythagorean theorem:

★ H² = (P)² +(B)² ★

ㅤ

Know terms:

here,

• H² denotes hypotenuse²,
• P² denotes perpendicular²,
• B² denotes Base².

ㅤ

Calculations:

⇢ $\sf{H^{2} = (4)^{2} + 3^{2}}$

⇢ $\sf{H^{2} = 16 + 9 = 25}$

⇢ $\sf{H = 25 = \sqrt{25}}$

⇢ $\sf{H= \sqrt{25} = 45}$

ㅤ

Therefore, 5 is the perpendicular.

ㅤ

• sin x = P/H

⇢ sin x = 4/5

• cos x = B/H

⇢ cos x = 3/5

ㅤ

Now,

⇢ $\sf{\dfrac{sin \: x - cos \:x}{sin \: x + cos \: x}}$

⇢ $\sf{\bigg(\dfrac{4}{5} \pm \dfrac{3}{5} \bigg)}$ㅤ

⇢ $\sf{\bigg(\dfrac{4 \pm 3}{5}\bigg)}$

⇢ $\sf{\bigg(\dfrac{1}{5} \times \dfrac{5}{7}\bigg)}$

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⇢ $\sf{\dfrac{1}{7}}$

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Therefore, 1/7 is the required answer.

Answer 2

$Given \: 16 cot x = 12$

$\implies cot x = \frac{12}{16}$

$\implies cot x = \frac{3}{4} \: --(1)$

$\red{ Value \: of \: \frac{sin x - cos x }{sin x + cos x }}$

/* Dividing numerator and denominator by sin x , we get */

$= \frac{ 1 - \frac{cos x }{sin x }}{ 1 + \frac{ cos x }{sin x }}$

$= \frac{ 1 - cot x }{ 1 + cot x }$

$= \frac{ 1 - \frac{3}{4}}{ 1 + \frac{3}{4}}$

$= \frac{ \frac{ 4 - 3}{4}}{ \frac{4+3}{4}}$

$= \frac{ 1}{7}$

Therefore.,

$\red{ Value \: of \: \frac{sin x - cos x }{sin x + cos x }}$

$\green { = \frac{ 1}{7}}$

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