Question

solve it in a method other than substitution ​

Answer 1

GOOD MORNING!!)

Sec²x Cosec²x - {Tan²x + Cot²x}

Replace Tan²x by Sin²x/Cos²x

And

Replace Cot²x by Cos²x/Sin²x

Sec²x Cosec²x - {Sin⁴x + Cos⁴x}/(Sin²x Cos²x)

Sec²x Cosec²x - {1 - 2Sin²x Cos²x }/(Sin²x Cos²x)

1/Sin²x Cos²x - {1 - 2Sin²x Cos²x}/(Sin²x Cos²x)

{1 - 1 + 2 Sin²x Cos²x }/ (Sin²x Cos²x)

2Sin²x Cos²x / Sin²x Cos²x

= 2

So, option A is correct!))

NOTE:-

(a⁴ + b⁴) = (a² + b²)² - 2(ab)²

Sin²x + Cos²x = 1