Question

if tan a = 3/4 then the value of tan ^2 A+ cot ^ 2 A is​

Answer 1

Answer:

337/144

Step-by-step explanation:

As per the provided information in the given question, we have:

• tan A = 3/4

We've been asked to calculate the value of tan²A + cot²A.

Firstly we need to calculate the value of cot A. cot θ is nothing but the reciprocal of tan θ. Hence if tan A is 3/4 then cot A would be 4/3.

⇒ cot A = 4/3 [Since, cot A = 1/tan A]

Now, according to the question :

⇒ tan²A + cot²A

⇒ (3/4)² + (4/3)²

⇒ 9/16 + 16/9

⇒ (81 + 256)/144

⇒ 337/144

Therefore, the required answer is 337/144.

$\rule{200}2$

Answer 2

Given: tan a = 3/4

To find: The value of tan² a + cot² a.

Solution:

• The value of (tan a) is given. So, the value of (tan² a) can be calculated as,

        $(\frac{3}{4} )^{2} = \frac{9}{16}$

• (cot) of an angle is the reciprocal of the (tan) of the same angle. So, (cot a) can be written as,

        $cot a = \frac{4}{3}$

• So, the value of (cot² a) can be calculated as,

        $(\frac{4}{3} )^{2} = \frac{16}{9}$

• Now, on substituting in the equation to be calculated,

        $tan^{2} a + cot^{2} a = \frac{9}{16} + \frac{16}{9}$

                              $=2.34$

Therefore, the value of tan² a + cot² a is 2.34.