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Question Number 81873 by zainal tanjung last updated on 16/Feb/20

$$\left|\begin{array}{ccc}{\sin }^{2}x& {\cos }^{2}x& 1\\ {\cos }^{2}x& {\sin }^{2}x& 1\\ -10& 12& 2\end{array}\right|=$$

Commented by john santu last updated on 16/Feb/20

$$\sin {}^{2}x(2\sin {}^{2}x-12)-\cos {}^{2}x(2\cos {}^{2}x+10)-(12\cos {}^{2}x+10\sin {}^{2}x)$$

Answered by MJS last updated on 16/Feb/20

$$=2({\sin }^{4}x-{\sin }^{2}x-{\cos }^{4}x+{\cos }^{2}x)=$$$$[\cos x=\sqrt{1-{\sin }^{2}x}]$$$$=0$$

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