Calculate the value of expresion: E(x)=\frac{\sin^6 x+\cos^6 x}{\sin^4 x+\cos^4 x} for \tan(x)=2

sunyerneq

sunyerneq

Answered question

2022-02-27

Calculate the value of expresion:
E(x)=sin6x+cos6xsin4x+cos4x
for tan(x)=2

Answer & Explanation

Jenson Mcculloch

Jenson Mcculloch

Beginner2022-02-28Added 9 answers

E(x)=sin6x+cos6xsin4x+cos4x=sin6x+cos6xcos6xsin4x+cos4xcos6x=tan6x+11cos2x(tan4x+1)
=cos2x26+124+1=11+tan2x6517=122+16517=1551317=1317
sin6x+cos6x=cos6x(sin6xcos6x+1)cos6x(tan6x+1)
jorgegalar0xk

jorgegalar0xk

Beginner2022-03-01Added 5 answers

tanx=2sinx2=cosx1sin2x4=cos2x1
=sin2x+cos2x4+1=15
sin6x+cos6xsin4x+cos4x=(45)3+(15)3(45)2+(15)2
=(43+1)5253(42+1)=1317

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