Evaluate the determinants in Exercises 1 and 2 -i - cos- -sin- sin- cos- - ii - x2-x-1 x-1- x-1 x-1 -

(i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos2 θ+ sin2 θ = 1 (ii) = (x2 − x + 1)(x + 1) − (x − 1)(x + 1) = x3 − x2 + x + x2 − x + 1 − (x2 − 1) = x3 + 1 − x ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Graph of Trigonometric Ratios

Evaluate the ...

Question

Evaluate the determinants in Exercises 1 and 2.

(i) (ii)

Open in App

Solution

(i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos² θ+ sin² θ = 1

(ii)

= (x² − x + 1)(x + 1) − (x − 1)(x + 1)

= x³ − x² + x + x² − x + 1 − (x² − 1)

= x³ + 1 − x² + 1

= x³ − x² + 2

Suggest Corrections

Similar questions

Evaluate the determinant
$(i)$ $∣ ∣ ∣ \begin{matrix} cos θ & - sin θ sin θ & cos θ \end{matrix} ∣ ∣ ∣$
$(i i)$ $∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

Q. Evaluate:

{sec}^{- 1} (\frac{x + 1}{x - 1}) + {sin}^{- 1} (\frac{x - 2}{x + 1})

Q. Evaluate:

lim x \to \frac{1}{\sqrt{2}}

\frac{x - cos ({sin}^{- 1} x)}{1 - tan ({sin}^{- 1} x)}

Q. Evaluate:

∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣

Evaluate the determinants.

$∣ ∣ ∣ \begin{matrix} c o s θ & - s i n θ s i n θ & c o s θ \end{matrix} ∣ ∣ ∣$

$∣ ∣ ∣ \begin{matrix} x^{2} - x +_{1} & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

Join BYJU'S Learning Program

Evaluate the determinants in Exercises 1 and 2. (i) (ii)

(i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos2 θ+ sin2 θ = 1 (ii) = (x2 − x + 1)(x + 1) − (x − 1)(x + 1) = x3 − x2 + x + x2 − x + 1 − (x2 − 1) = x3 + 1 − x2 + 1 = x3 − x2 + 2

Evaluate the determinants in Exercises 1 and 2.

(i) (ii)

(i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos² θ+ sin² θ = 1

(ii)

= (x² − x + 1)(x + 1) − (x − 1)(x + 1)

= x³ − x² + x + x² − x + 1 − (x² − 1)

= x³ + 1 − x² + 1

= x³ − x² + 2