Question

if 4 cot theta is equals to 3 show that sin theta minus cos theta upon sin theta + cos theta is equals to one upon 7​

Answer 1

Answer:

1/7

Step-by-step explanation:

4 cotA = 3 → cotA = 3/4

$\small{ \implies \frac{sin \theta - cos\theta}{ sin \theta + cos\theta} } \\ \\ \implies \frac{ \frac{sin \theta - cos\theta}{sin \theta} }{ \frac{sin \theta + cos\theta}{sin \theta}} \\ \\ \implies \frac{ \frac{sin \theta}{sin \theta} - \frac{cos\theta}{sin \theta} }{ \frac{sin \theta}{sin\theta} + \frac{cos\theta}{sin \theta} } \\ \\ \implies \small{ \frac{1 - cot\theta}{1 + cot \theta}}$

$\implies \frac{1-\frac{3}{4}}{1+\frac{3}{4}} \\\\\implies \frac{\frac{4-3}{4}}{\frac{1+3}{4}} \\\\\implies \frac{1}{7}$

Proved.

Answer 2

Answer:

1/7

Step-by-step explanation:

Given, 4 cotø = 3

cot ø = 3/4

To find: (sinø - cosø)/(sinø + cosø) = 1/7

Solution:

(sinø - cosø)/(sinø + cosø) = 1/7

Divide both numerator and denominator by cosø on L.H.S.

[(sinø - cosø)/cosø]/[(sinø + cosø)/cosø] = 7

(sinø/cosø - 1)/(sinø/cosø + 1) = 1/7

sinø/cosø = tanø

(tan ø - 1)/(tanø + 1) = 1/7

cotø = 1/tanø

(1/cotø - 1)/(cotø + 1) = 1/7

(1/3/4 - 1)/(1/3/4 + 1) = 1/7

(4/3 - 1)/(4/3 + 1) = 1/7

(1/3)(7/3) = 1/7

1/7 = 1/7