Question

18. यदि tan • + cot •=2 तो theta का मान ज्ञात करें ?
(a) 45°
(b) 60°
(c) 90°
(d) 30°​

Answer 1

Answer:

45°

Step-by-step explanation:

tanA + cotA = 2

⇒tanA + 1/tanA = 2 [cotA = 1/tanA]

⇒a + 1/a = 2          [let tanA = a]

 ⇒(a² + 1)/a = 2

⇒ a² + 1 = 2a

  ⇒a² - 2a + 1 =0

  ⇒a² - a - a + 1 = 0

  ⇒a(a - 1) - (a - 1) = 0

  ⇒(a - 1)(a - 1) = 0

  ⇒ (a - 1)² = 0

a - 1 = 0      ⇒ a = 1

                  ∴ tanA = 1

                     tanA = tan45°

                          A = 45°

Answer 2

Given :-

$\bullet\sf tan \theta + cot\theta = 2$

To Find :-

$\theta$

Solution :-

We know that

$\bf cot A = \dfrac{1}{\tan a}$

Now,

$\sf A+ \dfrac{1}{A} =2$

$\sf \dfrac{a\times a + 1}{a} = 2$

$\sf\dfrac{a^{2} + 1}{a} =2$

$\sf a^2 + 1 = 2a$

$\sf a^2 - 2a + 1 =0$

$\sf a^2 - a - a + 1 = 0$

$\sf (a-1),(a-1) = 0$

a - 1 = 0

a = 0 +1

a = 1

tan A = 1 = 45°