MHT CET · Maths · Trigonometric Ratios & Identities

\(\frac{\cos 12^{\circ}-\sin 12^{\circ}}{\cos 12^{\circ}+\sin 12^{\circ}}+\frac{\sin 147^{\circ}}{\cos 147^{\circ}}=\)

A -2
B 0
C -1
D 1

Verified Solution

Answer & Solution

Correct Answer

(B) 0

Step-by-step Solution

Detailed explanation

\(\frac{\cos 12^{\circ}-\sin 12^{\circ}}{\cos 12^{\circ}+\sin 12^{\circ}}+\frac{\sin 147^{\circ}}{\cos 147^{\circ}}\)
\(=\frac{\cos 12^{\circ}-\cos 78^{\circ}}{\cos 12^{\circ}+\cos 78^{\circ}}+\tan 147^{\circ}\)
\(=\frac{-2 \sin 45^{\circ} \sin \left(-33^{\circ}\right)}{2 \cos 45^{\circ} \cos 33^{\circ}}+\tan \left(180^{\circ}-33^{\circ}\right)=\tan 45^{\circ} \tan 33^{\circ}-\tan 33^{\circ}\)
\(=\tan 33^{\circ}-\tan 33^{\circ}=0\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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