If sin x = 1/2, then find the value of (sec⁴x + cosec⁴x) - (tan⁴x +cot⁴x).

26/3

We are given that :-

sin x = \(\frac{1}{2}\)

{ we know, sin30º = \(\frac{1}{2}\) }

So,  x = 30º

Now,

( sec4 x + cosec4 x ) - ( tan4 x + cot4 x )

= ( sec4 30º + cosec4 30º ) - ( tan4 30º + cot4 30º )

= ( \(\frac{16}{9}\) + 16 ) - ( \(\frac{1}{9}\) + 9 )

= ( \(\frac{160 }{9}\) ) - ( \(\frac{82}{9}\) ) 

= \(\frac{78}{9}\)

= \(\frac{26}{3}\)