Question

Cos theta + sin theta / sin theta - cos theta = 5/3 find tan theta

Answer 1

Given :-

$\: \: \: \: \: \: \: \: \bullet \: \sf \: \dfrac{sin \theta + cos \theta}{sin \theta - cos \theta} = \dfrac{5}{3}$

To find :-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: tan \theta$

SOLUTION :-

• Do cross multiplication

$\: \sf \: {(sin \theta + cos \theta)3} \ = {5} (sin \theta - cos \theta)$

$\: \sf \: {3sin \theta +3 cos \theta} \ = {5} sin \theta - 5cos \theta$

• Transposing like terms a side

$\sf \: \: 3sin \theta - 5sin \theta = \: - 5cos \theta - 3cos \theta$

$\sf \: \: - 2sin \theta = \: - 8cos \theta$

$\sf \: \: sin \theta = \: 4cos \theta$

$\sf \: \dfrac{sin \theta}{cos \theta} = 4$

From trigonometric relations sinA/cosA = tanA

$\underline{ \boxed{ \sf \: {tan \theta} = 4}}$

So, the Required answer tanθ is 4 .

Know more :-

ㅤㅤTrigonometric Identities:-

•sin²θ + cos²θ = 1

•sec²θ - tan²θ = 1

•csc²θ - cot²θ = 1

ㅤTrigonometric relations:-

•sinθ = 1/cscθ

•cosθ = 1 /secθ

•tanθ = 1/cotθ

•tanθ = sinθ/cosθ

•cotθ = cosθ/sinθ

ㅤㅤTrigonometric ratios:-

•sinθ = opp/hyp

•cosθ = adj/hyp

•tanθ = opp/adj

•cotθ = adj/opp

•cscθ = hyp/opp

secθ = hyp/adj