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```
if sin@+sin^2@=1 prove that cos^12@+3cos^10@+3cos^8@+cos^6@-1=0

```
6 years ago

```							given sin@=1-sin2@=cos2@therefore sin6@+3sin5@+3sin4@+sin3@-1={sin2@+sin@}2-1=1-1=0Thanks & RegardsSunil RaikwaraskIITian's Faculty
```
6 years ago
```							sin@+sin^2@=1=>sin@=1-sin^2@=cos^2@Nowcos^12@+3cos^10@+3cos^8@+cos^6@-1Using cos^2@=sin@ in this expression we getsin^6@+cos^6@+3cos^10@+3cos^8@-1=1-3sin^2@cos^2@+3cos^10@+3cos^8@-1=-3sin^2@cos^2@+3cos^10@+3cos^8@=-3sin^2@cos^2@+3sin^4@+3cos^10@=3sin^2@(sin^2@-cos^2@)+3cos^10@=-3sin^2@cos2@+3cos^10@=-3sin^2@cos2@+3cos^4@cos^6@=-3sin^2@cos2@+3sin^2@cos^6@=3sin^2@(cos^6@-cos2@)=3sin^2@(sin^2@cos^2@-cos2@)=3sin^2@(cos^2@sin^2@-cos^2@+sin^2@)=3sin^2@{cos^2@(sin^2@-1)+sin^2@}=3sin^2@{-sin@cos^2@+sin^2@}=3sin^2@{-sin@sin@+sin^2@}=3sin^2@{=sin^2@+sin^2@}=0Thanks & RegardsRinkoo GuptaAskIITians Faculty
```
6 years ago
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