Question

If tan θ = 3, then 4sinθ−cosθ/4sinθ+cosθ is equal to​

Answer 1

Given data:

$tan\theta=3$

To find:

The value of $\dfrac{4\:sin\theta-cos\theta}{4\:sin\theta+cos\theta}$

Step-by-step explanation:

• To find the value of the fraction, we divide both the numerator and the denominator by $cos\theta$ and convert the fraction into a fraction containing only $tan\theta$ terms.

• Remember that, $cos\theta\neq 0$

Now, $\dfrac{4\:sin\theta-cos\theta}{4\:sin\theta+cos\theta}$

$=\dfrac{\dfrac{4\:sin\theta-cos\theta}{cos\theta}}{\dfrac{4\:sin\theta+cos\theta}{cos\theta}}$

• since $cos\theta\neq 0$

$=\dfrac{\dfrac{4\:sin\theta}{cos\theta}-\dfrac{cos\theta}{cos\theta}}{\dfrac{4\:sin\theta}{cos\theta}+\dfrac{cos\theta}{cos\theta}}$

• since $\dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}$ where $c$ is not zero

$=\dfrac{4\:tan\theta-1}{4\:tan\theta+1}$

• since $tan\theta=\dfrac{sin\theta}{cos\theta}$

$=\dfrac{12-1}{12+1}$

• since $tan\theta=3$

$=\dfrac{11}{13}$

Answer:

$\boxed{\dfrac{4\:sin\theta-cos\theta}{4\:sin\theta+cos\theta}=\dfrac{11}{13}}$

Read more on Brainly.in

If sinθ = cos(2θ - 45°) then value of tanθ ...

- https://brainly.in/question/14287600

If tanA = x/y, prove

m sinA+ n cosA = √(m² + n²)

- https://brainly.in/question/15817313

Answer 2

Given data:

$tan\theta=3tanθ=3</p><p>$

To find:

$The value of \dfrac{4\:sin\theta-cos\theta}{4\:sin\theta+cos\theta}4sinθ+cosθ4sinθ−cosθ</p><p>$

Step-by-step explanation:

 terms.

Remember that, cos\theta\neq 0cosθ=0

Now, \dfrac{4\:sin\theta-cos\theta}{4\:sin\theta+cos\theta}4sinθ+cosθ4sinθ−cosθ

=\dfrac{\dfrac{4\:sin\theta-cos\theta}{cos\theta}}{\dfrac{4\:sin\theta+cos\theta}{cos\theta}}=cosθ4sinθ+cosθcosθ4sinθ−cosθ

since cos\theta\neq 0cosθ=0

=\dfrac{\dfrac{4\:sin\theta}{cos\theta}-\dfrac{cos\theta}{cos\theta}}{\dfrac{4\:sin\theta}{cos\theta}+\dfrac{cos\theta}{cos\theta}}=cosθ4sinθ+cosθcosθcosθ4sinθ−cosθcosθ

since \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}ca+b=ca+cb where cc is not zero

=\dfrac{4\:tan\theta-1}{4\:tan\theta+1}=4tanθ+14tanθ−1

since tan\theta=\dfrac{sin\theta}{cos\theta}tanθ=cosθsinθ

=\dfrac{12-1}{12+1}=12+112−1

since tan\theta=3tanθ=3

=\dfrac{11}{13}=1311

Answer:

\boxed{\dfrac{4\:sin\theta-cos\theta}{4\:sin\theta+cos\theta}=\dfrac{11}{13}}4sinθ+cosθ4sinθ−cosθ=1311

Read more on Brainly.in

If sinθ = cos(2θ - 45°) then value of tanθ ...

- https://brainly.in/question/14287600

If tanA = x/y, prove

m sinA+ n cosA = √(m² + n²)

- https://brainly.in/question/15817313