Question

if tan theta + cot theta =2 then find √tan^2 theta and cot^2 theta ​

Answer 1

Given :-

Tan Φ + Cot Φ = 2

Solution :-

Tan Φ + Cot Φ = 2

Squaring both sides ,

( TanΦ + CotΦ ) ^2 = ( 2 )^2

[Using Identity ( a + b )^2

= a^2 + 2ab + b^2 ]

Tan^2 Φ + 2 * Tan Φ * CotΦ + Cot^2 Φ = 4

[ As we know that ,CotΦ = 1/ Tan Φ ]

Tan^2 Φ + 2 * Tan Φ * 1 / TanΦ + Cot^2 = 4

Tan^2 + 2 + Cot^2 Φ = 4

Tan^2Φ + Cot^2Φ = 4 - 2

Tan^2 Φ + Cot^2 Φ = 2 .......eq( 1 )

Now ,

$\sqrt{ {tan}^{2} \: + {cot \: }^{2} }$ = ?

√ tan^2 + cot^2 = √2. [ from eq( 1 ) ]