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The expression (cos6θ + sin6θ - 1)(tan2θ + cot2θ + 2) + 3 is equal to:
Answer & Solution
Correct Answer:
Option
A
(cos6θ + sin6θ - 1)(tan2θ + cot2θ + 2) + 3
Put θ = 45°
= (cos645° + sin645° - 1)(tan245° + cot245° + 2) + 3
$$\eqalign{ & = \left( {\frac{1}{8} + \frac{1}{8} - 1} \right)\left( {1 + 1 + 2} \right) + 3 \cr & = - \frac{3}{4} \times 4 + 3 \cr & = 0 \cr} $$
Put θ = 45°
= (cos645° + sin645° - 1)(tan245° + cot245° + 2) + 3
$$\eqalign{ & = \left( {\frac{1}{8} + \frac{1}{8} - 1} \right)\left( {1 + 1 + 2} \right) + 3 \cr & = - \frac{3}{4} \times 4 + 3 \cr & = 0 \cr} $$
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