Question

if tan x + cot x = 2 find the value of tan²x+cot²x​

Answer 1

Answer:

4

Step-by-step explanation:

if

tan x+ cot x= 2

then tan^2 x+ cot^2 x=4

Answer 2

Given :-

• tan x + cot x = 2

To Find :–

• tan² x + cot² x = ?

Solution :–

We are given :-

$\sf \red{\: \: \: \: \: \: \: :\implies \tan(x) + \cot(x) = 2}$

• Squaring on both side : –

$\sf\: \: \: \: \: \: \: : \implies \{ \tan(x) + \cot(x) \}^{2} = {(2)}^{2}$

• Using identity :–

$\sf\red{\: \: \: \: \: \: \: : \implies \boxed{ \sf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}}$ㅤ

$\sf\: \: \: \: \: \: \: :\implies \tan^{2} (x)+ \cot^{2} (x) + 2 \tan(x) . \cot(x) = 4$

$\sf\: \: \: \: \: \: \: : \implies \tan^{2} (x)+ \cot^{2} (x) + 2 \tan(x) . \left \{ \dfrac{1}{ \tan(x) } \right \} = 4$

$\sf\: \: \: \: \: \: \: :\implies \tan^{2} (x)+ \cot^{2} (x) + 2= 4$

$\sf\: \: \: \: \: \: \: : \implies \tan^{2} (x)+ \cot^{2} (x) = 4 - 2$

$\sf\: \: \: \: \: \: \: : \implies \tan^{2} (x)+ \cot^{2} (x) = 2$

$\sf \red{\: \: \: \: \: \: \: : \implies \boxed{ \sf \tan^{2} (x)+ \cot^{2} (x) = 2 }}$

$\therefore\:\underline{\textsf{ Value of tan² x + cot² x is \textbf{2}}}$

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