if-sin-x-cos-x-sin-x-cos-x-1-4-find-the-value-of-F-sin-6-x-cos-6-x-

Question Number 190893 by mnjuly1970 last updated on 13/Apr/23

i f, \frac{s i n (x) - c o s (x)}{s i n (x) + c o s (x)} = \frac{1}{4}

\Rightarrow f i n d t h e v a l u e o f

F = {s i n}^{6} (x) + {c o s}^{6} (x) = ?

Answered by Frix last updated on 13/Apr/23

\Rightarrow \tan x = \frac{5}{3} \Rightarrow F = \frac{481}{1156}

Answered by mehdee42 last updated on 13/Apr/23

t a n x = \frac{5}{3}

F = ({s i n}^{2} x + {c o s}^{2} x) ({s i n}^{4} + {c o s}^{4} x - {s i n}^{2} {x c o s}^{2} x)

= {({s i n}^{2} x + {c o s}^{2} x)}^{2} - 3 {s i n}^{2} {x c o s}^{2} x

= 1 - \frac{3}{4} {s i n}^{2} 2 x = 1 - \frac{3}{4} \times {(\frac{2 t a n x}{1 + {t a n}^{2} x})}^{2} = \dots

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