If sin x + sin^2 x = 1,then the value of cos^ | vedclass

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(C) Given,$\sin x + \sin^2 x = 1$. This implies $\sin x = 1 - \sin^2 x$,so $\sin x = \cos^2 x$. Now,consider the expression: $E = \cos^{12} x + 3\cos^

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(C) Given,$\sin x + \sin^2 x = 1$. This implies $\sin x = 1 - \sin^2 x$,so $\sin x = \cos^2 x$. Now,consider the expression: $E = \cos^{12} x + 3\cos^{10} x + 3\cos^8 x + \cos^6 x - 2$. Substituting $\cos^2 x = \sin x$,we get: $E = (\sin x)^6 + 3(\sin x)^5 + 3(\sin x)^4 + (\sin x)^3 - 2$. This can be rewritten as: $E = (\sin^2 x)^3 + 3(\sin^2 x)^2(\sin x) + 3(\sin^2 x)(\sin x)^2 + (\sin x)^3 - 2$. Using the binomial expansion $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$,where $a = \sin^2 x$ and $b = \sin x$: $E = (\sin^2 x + \sin x)^3 - 2$. Since $\sin^2 x + \sin x = 1$,we have: $E = (1)^3 - 2 = 1 - 2 = -1$.

If $\sin x + \sin^2 x = 1$,then the value of $\cos^{12} x + 3\cos^{10} x + 3\cos^8 x + \cos^6 x - 2$ is equal to

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