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If Delta(1) =|{:(x, sin theta, cos theta...

If `Delta_(1) =|{:(x, sin theta, cos theta),(-sin theta, -x, 1),(cos theta, 1,x):}|` and `Delta_(2) =|{:(x, sin 2theta, cos 2theta),(-sin 2theta, -x, 1),(cos 2theta, 1,x):}|, x ne 0`, then for all `theta in (0, pi/2)`, Then, `Delta_(1) + Delta_(2) =-2x^(k)`. The value of k is ________.

A

`Delta_1+Delta_2=-2(x^3+x-1)`

B

`Delta_1-Delta_2=-2x^3`

C

`Delta_1+Delta_2=-2x^3`

D

`Delta_1-Delta_2=x(cos 2theta - cos 4 theta)`

Text Solution

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The correct Answer is:
C
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