Question

if tan A + Cot A =2 find the value of tan ^99 A+cot^99 A
plz help ​

Answer 1

Answer:

Answer is 1

Step-by-step explanation:

tanA +CotA =2

1. tanA+1/tanA =2
2. tan^2A+1=2tanA
3. tan^2A-2tanA+1=0
4. tan^2A -tanA -tanA +1=0
5. tanA(tanA-1) -1(tanA-1) =0
6. (tanA -1)(tanA-1) =0
7. tana=1and cotA=1
8. tan^99A+cot^99=1

Answer 2

Answer :

Value of $\sf{tan^{99}+cot^{99}}$ is 2.

Solution :

Given that ,

tanA + cotA = 2

We know ,

${\boxed{\sf{cotA=\dfrac{1}{tanA}}}}$

$\to\sf{tanA+cotA=2}$

$\to\sf{tanA+\dfrac{1}{tanA}=2}$

$\to\sf{\dfrac{tan^2A+1}{tanA}=2}$

$\to\sf{tan^2A+1=2tanA}$

$\to\sf{tan^2A-2tanA+1=0}$

$\to\sf{(tanA-1)^2=0}$

$\to\sf{tanA-1=0}$

$\to\sf{tanA=1}$

★Now find the value of $\sf{tan^{99}+cot^{99}}$

$\sf{tan^{99}+cot^{99}}$

$\to\sf{tan^{99}+\dfrac{1}{tanA^{99}}}$

• Put tanA = 1.

$\to\sf{1^{99}+\dfrac{1}{1^{99}}}$

$\to\sf{1+1}$

$\to\sf{2}$

__________________

★ Some trigonometric formulas :-

★ sin2∅ = 2sin∅ cos∅

★ cos2∅ = 2cos²∅ -1

★ $\sf{tan\theta=\dfrac{1-cos2\theta}{1+cos2\theta}}$

★ 1-co2∅ = 2sin²∅

★ $\sf{tan2\theta=\dfrac{2tan\theta}{1-tan^2\theta}}$

★ $\sf{tan3\theta=\dfrac{3tan\theta-tan^3\theta}{1-3tan^2\theta}}$

★ $\sf{1+cos2\theta=2cos^2\theta}$