Question

Ir tan A + cot A = 2 then what is the value of tan^2 A + cot^2 A.​

Answer 1

[tex]\mathfrak{ \huge{Answer:-} } \\tan A + cotA = 2 \\Squaring \: on \: both \: the \: sides \\ {(tanA + cotA)}^{2} = {(2)}^{2} \\ {(tanA)}^{2} + {(cotA)}^{2} + 2(tanA)(cotA) = 4 \\ {tan}^{2}A + {cot}^{2} A + 2 \times \frac{sinA}{cosA} \times \frac{cosA}{sinA} = 4 \\ {tan}^{2} A + {cot}^{2}A + 2 = 4 \\ {tan}^{2}A + {cot}^{2}A = 4 - 2 \\ \boxed{ \boxed{ \large{\bold{ {tan}^{2}A + {cot}^{2} A = 2 }} } } [/tex]