Question

Sec x - cosec x =4 then find the value of sinx - cosx= ?

Answer 1

Step-by-step explanation:

hey mate

if started the basics of trignometry it will be helpful

so here is your answer

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If sin x + cosec x = 4, then what is sin^10 x + cosec^10 x?

sin x + cosec x = 4, or

sin x + 1/sin x = 4, or

sin^2 x + 1 = 4 sin x, or

sin^2 x - 4 sin x+ 1 = 0. Let sin x = m, Then

m^2–4m+1 = 0

m1 = [4+(16–4)^0.5]/2

= [2+√3], or

m2 = [2-√3]

sin^10 x + cosec^10 x = [2+√3]^10 + 1/[2+√3]^10

= [2+√3]^10 + [2-√3]^10/[2+√3]^10*[2-√3]^10

= [2+√3]^10 + [2-√3]^10

= 524174 + 1.9^(-6)

= 524174

OR

sin^10 x + cosec^10 x = [2-√3]^10 + 1/[2-√3]^10

= [2-√3]^10 + [2+√3]^10/[2-√3]^10*[2+√3]^10

= [2-√3]^10 + [2+√3]^10

= 524174 + 1.9^(-6)

= 524174

sin^10 x + cosec^10 x = 524174

hope it helps

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