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

1.	Mark the tick against the correct answer in the following:\(\begin{vmatrix} cos 70^\circ & sin 20^\circ\\[0.3em] sin 70^\circ & cos 20^\circ \\[0.3em] \end{vmatrix}\) = ?A. 1B. 0C. cos 50°D. sin 50°
Answer» Correct answer B. 0 To find: value of \(\begin{vmatrix} cos 70^\circ & sin 20^\circ\\[0.3em] sin 70^\circ & cos 20^\circ \\[0.3em] \end{vmatrix}\) Formula used: (i) cos\(\theta\) = sin(90 - \(\theta\)) We have \(\begin{vmatrix} cos 70^\circ & sin 20^\circ\\[0.3em] sin 70^\circ & cos 20^\circ \\[0.3em] \end{vmatrix}\) On expanding the above, ⇒ {cos 70°} {cos 20°} – {sin 70°} {sin 20°} On applying formula cos\(\theta\) = sin(90 - \(\theta\) ) ⇒ {sin (90 – 70)} {sin (90 – 20)} - {sin 70°} {sin 20°} ⇒ {sin 20°} {sin 70°} - {sin 70°} {sin 20°} = 0

Mark the tick against the correct answer in the following:\(\begin{vmatrix} cos 70^\circ & sin 20^\circ\\[0.3em] sin 70^\circ & cos 20^\circ \\[0.3em] \end{vmatrix}\) = ?A. 1B. 0C. cos 50°D. sin 50°

Answer»

Correct answer B. 0

To find: value of \(\begin{vmatrix} cos 70^\circ & sin 20^\circ\\[0.3em] sin 70^\circ & cos 20^\circ \\[0.3em] \end{vmatrix}\)

Formula used: (i) cos\(\theta\) = sin(90 - \(\theta\))

We have \(\begin{vmatrix} cos 70^\circ & sin 20^\circ\\[0.3em] sin 70^\circ & cos 20^\circ \\[0.3em] \end{vmatrix}\)

On expanding the above,

⇒ {cos 70°} {cos 20°} – {sin 70°} {sin 20°}

On applying formula cos\(\theta\) = sin(90 - \(\theta\) )

⇒ {sin (90 – 70)} {sin (90 – 20)} - {sin 70°} {sin 20°}

⇒ {sin 20°} {sin 70°} - {sin 70°} {sin 20°}

= 0