|(sin 23°, -sin27°),(cos23°, cos 7°)| = ?

Question

Mark the tick against the correct answer in the following:

\(\begin{vmatrix} sin 23^ \circ & -sin7^ \circ \\[0.3em] cos23^ \circ & cos7^ \circ \end{vmatrix}\) = ?

|(sin 23°, -sin27°),(cos23°, cos 7°)| = ?

A. \(\frac{\sqrt{3}}{2}\)

B. \(\frac{1}{2}\)

C. sin 16°

D. cos 16°

Answer 1

Correct answer B \(\frac{1}{2}\)

To find: value of \(\begin{vmatrix} sin 23^ \circ & -sin7^ \circ \\[0.3em] cos23^ \circ & cos7^ \circ \end{vmatrix}\)

Formula used: (i) sin(A + B) = sin A cos B + cos A sin B

We have, \(\begin{vmatrix} sin 23^ \circ & -sin7^ \circ \\[0.3em] cos23^ \circ & cos7^ \circ \end{vmatrix}\)

on expanding the above,

On expanding the above, 

⇒ (sin 23°) (cos 7°) – (cos 23°) (-sin 7°) 

⇒ (sin 23°) (cos 7°) + (cos 23°) (sin 7°) 

On applying formula sin(A + B) = sin A cos B + cos A sin B

= sin (23 + 7) = sin (30°)

= \(\frac{1}{2}\)