Question : If $\cos\left(40^\circ+x\right)=\sin 30^\circ$, then the value of $x$ is:
Option 1: $22^\circ$
Option 2: $20^\circ$
Option 3: $19^\circ$
Option 4: $23^\circ$
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Correct Answer: $20^\circ$
Solution : $\cos \left(40^\circ+x\right)=\sin 30^\circ$ ....(1) Now we know that $\sin(90^\circ -x)= \cos x^\circ$ $\therefore$ Equation (1) becomes ⇒ $\cos \left(40^\circ+x\right)=\sin (90^\circ-60^\circ)$ ⇒ $\cos \left(40^\circ+x\right)=\cos 60^\circ$ ⇒ $(40^\circ+x) = 60^\circ$ $\therefore x=20^\circ$ Hence, the correct answer is $20^\circ$.
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