Trigonometry practice problems.

Q1. If $$ \sin\theta + \cos\theta = 1 $$ then $$ \sin\theta \cos\theta =\;? $$
Options: (1) 0  (2) 1  (3) 2  (4) \(\frac{1}{2}\)

Answer: 0


Q2. Evaluate $$ 2(\sin^6 \theta + \cos^6 \theta) - 3(\sin^4 \theta + \cos^4 \theta) + 1 $$
Options: (1) 2  (2) 0  (3) 4  (4) 6

Answer: 0


Q3. If $$ \csc A + \cot A = \frac{11}{2}, $$ then $$ \tan A =\;? $$
Options: (1) \(\frac{22}{117}\)   (2) \(\frac{2}{11}\)   (3) \(\frac{117}{22}\)   (4) \(\frac{44}{117}\)

Answer: \(\frac{44}{117}\)


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