![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given the vector α = (cosx, SiNx), B = (√ 2, √ 2), a · B = 8 / 5, then the value of Tan (x - π / 4) is
ab=√2cosx+√2sinx=8/5
SiNx + cosx = (4 / 5) √ 2
So (SiNx + cosx) ^ 2 = 32 / 25
That is, 1 + 2sinxcosx = 32 / 25, then 2sinxcosx = 7 / 25
Then (SiNx cosx) ^ 2 = 1-2sinxcosx = 1-7 / 25 = 18 / 25
SiNx cosx = ± (3 / 5) √ 2
tan(x-π/4)=(tanx-1)/(tanx+1)=(sinx-cosx)/(sinx+cosx)
=[±(3/5)√2]/[(4/5)√2]
=±3/4
RELATED INFORMATIONS
- 1. Given the vector a = (1 / 2, √ 3 / 2), B = (cosx, SiNx). If a · B = 2cos [(12K π + 13 π) / 6 + x] (K ∈ z), find the value of Tan (x + 5 π / 12) Only the answer is OK
- 2. Given that the vector a = (SiNx, 2) the vector b = (|, - cosx), and the vector a is perpendicular to the vector B. 1::: find the value of TaNx 2: find the value of Tan (x-wu / 4),
- 3. Given the vector a = (SiNx, 2), B = (1, - cosx), and a is perpendicular to B, find the value of TaNx and Tan (x-card / 4)
- 4. Given the vector a = (SiNx, 1), B = (cosx, 1), X ∈ R. (1) when x = π 4, find the coordinates of vector a + B; (2) if the function f (x) = | a + B | 2 + m is an odd function, find the value of real number M
- 5. Let f (SiNx) = cos2x, then f (1 / 3) is equal to?
- 6. sin3x/sinx+cos3x/cosx
- 7. cos3x/2×cosx/2-sin3x/2×sinx/2
- 8. How to solve sin3x-cos3x-sinx + cosx?
- 9. Let a focus of the ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) coincide with the focus of the parabola C: y ^ 2 = 8x, the eccentricity e = 2 radical 5 / 5, the right focus f passing through the ellipse be a straight line L not coincident with the coordinate axis, intersecting the ellipse at two points a and B. let m (1,0), and (MA vector + MB vector) ⊥ AB vector, find the equation of the straight line L
- 10. It is known that the parabola y = x ^ 2-2 and the ellipse x ^ 2 / 4 + y ^ 2 = 1 have four intersections If the four points are in a circle, the equation of the circle is
- 11. If x is less than or equal to 90 degrees, greater than or equal to 0 degrees, SiNx * cosx = 1 / 2, then 1 / (1 + SiNx) + 1 / (1 + cosx) =? Detailed process! I'll collect it in an hour
- 12. Find the range of function f (x) = SiNx sinxcosx + cosx, X ∈ (π / 2,3 π / 2)
- 13. (SiNx + cosx) / (SiNx cosx) = 2, then sinxcosx =?
- 14. X is (0, π / 2). If sinxcosx = 1 / 2, find the value of 1 / (1 + SiNx) + 1 / (1 + cosx)
- 15. Given SiNx cosx = 1 / 2, the value of sinxcosx is____ (process!)
- 16. It is known that sinxcosx = 60 / 169 and π / 4
- 17. Given that SiNx times cosx is equal to 1 / 8, and Pie / 4 is less than X and Pie / 2, what is cosx SiNx equal to?
- 18. F (x) = the maximum of cosx - (SiNx) ^ 2
- 19. What is the maximum value of F (x) = SiNx + cosx? (the value range of X is R)
- 20. What is the maximum value of F (x) = sinx-2 / cosx + 1? 2, find the solution set of inequality | root x-1-2 | 1 3. Given the equation of circle (x-1) ^ 2 + (Y-1) ^ 2 = 8 and the straight line is x + y = 0, how many points on the circle whose distance to the straight line is equal to the root 2? For the first question, with options, a, 3 / 4, B, - 4 / 5, C-3 / 4, D, 4 / 5