Question

If $A = {30^ \circ }$and$B = {60^ \circ }$, then $cos\left( {A + B} \right) = cosAcosB-sinAsinB$. If the above statement is true, write $1$ and if false then write $0$.

Answer 1

Hint:Start by putting the values of $A$ and $B$ and in the formula and solve by taking the trigonometric values.

Complete step-by-step answer:
L.H.S
$\Rightarrow cos\left( {A + B} \right)$
$\Rightarrow \;cos\left( {{{60}^ \circ } + {{30}^ \circ }} \right)$
$\Rightarrow \;cos{90^ \circ } = {\text{ }}0$
R.H.S
$\Rightarrow cosAcosB-sinAsinB$
$\Rightarrow \;cos{60^ \circ }cos{30^ \circ }-sin{0^ \circ }sin{30^ \circ }$
$\frac{{\sqrt 3 }}{4} - \frac{{\sqrt 3 }}{4} = 0$
Since, LHS=RHS
Therefore, the answer is TRUE which in this question is equal to $1$.
Note: We started by assigning the values of A and B in the given equation and then simplifying to get the answer.