Question

Find the value of (tan@-cot@)^2+2​

Answer 1

Answer:

(tanA-cotA)²+2=1

Step-by-step explanation:

(tanA-cotA)²+2

   ↓       ↓

These two are in the form of $(a-b)^{2}$ and we know that $(a-b)^{2} =a^{2}+b^{2}-2ab$

Here,

$a^{2} =tanA$

$b^{2} =cotA$

(tanA-cotA)²=(tanA)²+(cotA)²-2(tanA)(cotA)+2

                    =tan²A+cot²A-2(1)+2 [∴tanA reciprocal is 1/cotA and   cotA reciprocal is tanA,if the main trigonometry and its reciprocal are in multiplication we can cancel and write as 1]

                    =tan²A+cot²A-2+2

                    =tan²A+cot²A

                    =sin²A/cos²A+cos²A/sin²A [∴because tanA=sinA/cosA and cotA=cosA/sinA]

                    =sin²A+cos²A/cos²A+sin²A

                    =1/1 [∴sin²A+cos²A=1]

                    =1

∴Please mark it as brainlist answer