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

$$$$$$if,\frac{sin\left(x\right)-cos\left(x\right)}{sin\left(x\right)+cos\left(x\right)}=\frac{1}{4}$$$$\Rightarrow findthevalueof$$$$$$$$\mathrm{F}={sin}^6\left(x\right)+{cos}^6\left(x\right)=?$$$$$$

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

$$tanx=\frac{5}{3}$$$$F=({sin}^{2}x+{cos}^{2}x)({sin}^4+{cos}^{4}x-{sin}^2{xcos}^{2}x)$$$$={({sin}^{2}x+{cos}^{2}x)}^2-3{sin}^2{xcos}^{2}x$$$$=1-\frac{3}{4}{sin}^{2}2x=1-\frac{3}{4}\times {\left(\frac{2tanx}{1+{tan}^{2}x}\right)}^2=...$$

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