If sin x +sin^2 x=1 then find the value of cos^8 x +2cos^6 x+cos^4 x
(INDEX;^2 : means to the power of)
If sin x +sin^2 x=1 then find the value of cos^8 x +2cos^6 x+cos^4 x
(INDEX;^2 : means to the power of)
Keshavendu Mondal , 6 Years ago
Grade 10
10 grade maths> If sin x +sin^2 x=1 then find the value o...
1 AnswersArun
Last Activity: 6 Years ago
Sinx +sin²x=1
sinx=1-sin²x
sinx=cos²x
sin²x=cos⁴x
so,
cos^8x+2cos^6x+cos⁴x
=cos⁴x(cos⁴x+2cos²x+1)
=sin²x (sin²x+2sinx+1)
=sin⁴x+2sin³x+sin²x
=sin⁴x+sin³x+sin³x+sin²x
=sin²x(sin²x+sinx)+ sinx(sin²x+sinx)
=sin²x×(1)+ sinx(1)
=sin²x+sinx
= 1
sinx=1-sin²x
sinx=cos²x
sin²x=cos⁴x
so,
cos^8x+2cos^6x+cos⁴x
=cos⁴x(cos⁴x+2cos²x+1)
=sin²x (sin²x+2sinx+1)
=sin⁴x+2sin³x+sin²x
=sin⁴x+sin³x+sin³x+sin²x
=sin²x(sin²x+sinx)+ sinx(sin²x+sinx)
=sin²x×(1)+ sinx(1)
=sin²x+sinx
= 1
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