Value of $\tan 1^\circ \tan 2^\circ ... \tan 89^\circ$.

Answer: 1. Pairs like $\tan 1 \times \tan 89$ become 1 because $\tan 89 = \cot 1$. All terms cancel to 1.

If $\sec \theta + \tan \theta = 2$, find $\sec \theta$.

Answer: 1.25. We know $\sec - \tan = 1/(\sec + \tan) = 1/2 = 0.5$. Adding the two equations: $2\sec = 2.5 \Rightarrow \sec = 1.25$.

Master trigonometric values, the CAST rule (quadrants), and fundamental identities to solve advanced math problems in SSC CGL.

$\sin \theta = P/H$ , $\cos \theta = B/H$ , $\tan \theta = P/B$
The Master Table: Memorize values for 0, 30, 45, 60, and 90.
Complementary: $\sin(90-\theta) = \cos \theta$ , $\tan(90-\theta) = \cot \theta$ .

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