Q.Find the value of: $\tan135° + \cot150°$.

Both angles are written as $180°$ minus a standard angle, and the supplementary-angle sign rule (tangent and cotangent both flip sign) applies to each.

Step 1 — write each angle as $180°$ minus a standard angle.

Step 2 — apply the supplementary-angle sign rule (tangent and cotangent flip sign under $180°-\theta$, same rule as cosine).

$\tan135° = \tan(180°-45°) = -\tan45° = -1$ …

Applying the sine sign-rule (unchanged sign) to tangent or cotangent by mistake is a frequent error — only sine keeps its sign under $180°-\theta$; cosine, tangent, and cotang …