# 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

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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.

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.

Last updated date: 21st Sep 2023

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