Trigonometry IV

Geometry Level 2

What Is the Determinant of Matrix A A ?

A = [ sin ⁡ x cos ⁡ 2 x 1 sin ⁡ x cos ⁡ x 0 sin ⁡ x 1 1 ] A=\begin{bmatrix} \sin x & \cos^2x & 1 \\ \sin x & \cos x & 0 \\ \sin x & 1 & 1 \end{bmatrix}

s i n 3 x sin^3 x c o s 3 x cos^3 x t a n 3 π 2 tan^3 \frac{\pi}{2} s i n 2 π 4 sin^2 \frac{\pi}{4}

Gabriel Merces by Gabriel Merces , 23, Brazil

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3 solutions

Faiz Kumar
Jun 16, 2014

Expanding along C3, we get sinx-sinxcosx+sinxcosx-sinxcos²x= sinx-sinxcos²x= sinx(1-cos²x)= sinx*sin²x= sin³x

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Replace 1st raw by subtracting 3rd raw from first. 1st row now is <........> 0.... { Cos^2(x) - 1 }...0.
Only reverse diagonal now is..... - ( Cos^2(x) - 1 ) Sin(x) 1 = Sin^3(x).,

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Mayur Gohil
May 19, 2014

try establishing maximum zeros in the given matrix using only row or column addition or subtraction operations and then find determinant . your answer is there with you

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