The value of the expression (cos6θ + sin6θ - 1)(tan2θ + cot2θ + 2) is:
A. -3
B. 0
C. -1
D. 1
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & \left( {{{\cos }^6}\theta + {{\sin }^6}\theta - 1} \right)\left( {{{\tan }^2}\theta + {{\cot }^2}\theta + 2} \right) \cr & {\text{Put }}\theta = {45^ \circ } \cr & = \left( {{{\cos }^6}{{45}^ \circ } + {{\sin }^6}{{45}^ \circ } - 1} \right)\left( {{{\tan }^2}{{45}^ \circ } + {{\cot }^2}{{45}^ \circ } + 2} \right) \cr & = \left( {\frac{1}{8} + \frac{1}{8} - 1} \right)\left( {1 + 1 + 2} \right) \cr & = \frac{{ - 3}}{4} \times 4 \cr & = - 3 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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