Mark the tick against the correct answer in the following:\(\begin{vma

1.	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» 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°) = \(\frac{1}{2}\)

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»

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°)

= \(\frac{1}{2}\)