Question

If sin A = 1/4, then tan A/2
+ cot A/4 =​

Answer 1

Answer:

= 17/16 cosθ. please make sure it is correct. sorry for the delay.

Answer 2

$\text{For } sinA = \dfrac{1}{4} \Rightarrow \dfrac{tan A}{2} + \dfrac{cot A}{4} = \dfrac{17}{4\sqrt{15} }$

Step-by-step explanation:

Given: $sinA = \frac{1}{4}$

To Find: the value of $\frac{tan A}{2} + \frac{cot A}{4}$

Solution:

• Finding the value of $\frac{tan A}{2} + \frac{cot A}{4}$

We have the expression $\frac{tan A}{2} + \frac{cot A}{4}$ such that we can write,

$\Rightarrow \dfrac{tan A}{2} + \dfrac{cot A}{4}$

$\Rightarrow \dfrac{1}{2} \Big( \dfrac{sin A}{cos A} \Big) + \dfrac{1}{4} \Big( \dfrac{cos A}{sin A} \Big)$

$\Rightarrow \dfrac{2sin^2 A + cos^2A}{4 \ sinA \ cos A}$

$\Rightarrow \dfrac{sin^2 A + (sin^2 A + cos^2A)}{4 \ sinA \ cos A}$

$\Rightarrow \dfrac{sin^2 A + 1}{4 \ sinA \ cos A} \ \ \ \ \because sin^2 A + cos^2A = 1$

$\Rightarrow \dfrac{sin^2 A + 1}{4 \ sinA \ ( \sqrt{1 - sin^2 A} )} \ \ \ \ \because cosA = \sqrt{1 - sin^2 A}$

Now, substituting the given value of sin A, we get,

$\Rightarrow \dfrac{(\frac{1}{4})^{2} + 1}{4 \ (\frac{1}{4}) \ ( \sqrt{1 - (\frac{1}{4})^{2}} )}$

$\Rightarrow \dfrac{17}{4 \sqrt{15} }$

Hence, for $sinA = \dfrac{1}{4} \Rightarrow \dfrac{tan A}{2} + \dfrac{cot A}{4} = \dfrac{17}{4\sqrt{15} }$