Question

23. Usman asked her classmate Mamta to calculate the value of
"sin 60° cos 30° + cos 60° sin 30.
Mamta calculated the value as shown below:
sin 60° cos 30° + cos 60° sin 30°= sin (60°+ 309) + cos (60° + 309)
= sin 90° + cos 90°
= 1 + 0
= 1
i.
Examine if Mamta's calculation is correct or not.
ii. If not, point out the inaccuracy and give the correct calculation. If yes, calculate if
the answer will still be "1" if angles 60° and 30° in the equation were changed to
45°
​

Answer 1

Answer:

${ \huge{ \red{ \rm{Solution : }}}}$

$: { \implies{ \sf{sin60 . cos30 + cos60 . sin30}}} \\ \\ : { \implies{ \sf{ \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} + \frac{1}{2} \times \frac{1}{2} }}} \\ \\ : { \implies{ \sf{ \frac{3}{4} + \frac{1}{4} }}} \\ \\ : { \implies{ \sf{ \frac{3 + 1}{4} }}} \\ \\ : { \implies{ \sf{ \frac{4}{4} }}} \\ \\ : { \implies{ \sf{1}}}$

Yes, Mamatha calculation is also correct

More information:

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm Not Defined \\ \\ \rm cosec A & \rm Not Defined & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm Not Defined \\ \\ \rm cot A & \rm Not Defined & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}$