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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