gaokao 2010 Q19

gaokao · China · shanghai-arts Trig Proofs Trigonometric Identity Simplification
19. (Total Score: 12 points) Given $0 < x < \frac { \pi } { 2 }$ , simplify: $\lg \left( \cos x \cdot \tan x + 1 - 2 \sin ^ { 2 } \frac { x } { 2 } \right) + \lg \left[ \sqrt { 2 } \cos \left( x - \frac { \pi } { 4 } \right) \right] - \lg ( 1 + \sin 2 x )$ .
(10 points) To investigate whether elderly people in a certain region need help from volunteers, a simple random sample of 500 elderly people from the region was surveyed, with results shown in the table: 
19. (Total Score: 12 points)\\
Given $0 < x < \frac { \pi } { 2 }$ , simplify: $\lg \left( \cos x \cdot \tan x + 1 - 2 \sin ^ { 2 } \frac { x } { 2 } \right) + \lg \left[ \sqrt { 2 } \cos \left( x - \frac { \pi } { 4 } \right) \right] - \lg ( 1 + \sin 2 x )$ .
Paper Questions
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