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Gaurav Seth 5 years, 1 month ago
Q : Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (-4, 0, 0) is equal to 10?
Answer:

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Gaurav Seth 5 years, 1 month ago
LHS = sin²(6x) - sin²(4x)
Use the formula,
(a² - b²) = (a - b)(a + b)
= (sin6x -sin4x)(sin6x +sin4x)
Now,
Use the formula,
sinC + sinD = 2sin(C+D)/2.cos(C-D)/2
sinC - sinD = 2cos(C+D)/2.sin(C-D)/2
={2cos(6x+4x)/2.sin(6x-4x)/2}{2sin(6x+4x)/2.cos(6x-4x)/2}
={2cos5x.sinx}{2sin5x.cosx}
={2sin5x.cos5x}{2sinx.cosx}
Use the formula,
sin2A = 2sinA.cosA
= sin2(5x).sin2(x)
= sin10x.sin2x =RHS
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Gaurav Seth 5 years, 1 month ago
Answer:
1) sec X = 13/5
x lies in 4th quadrant.
cos X = 1/ secx
2) So, cos x = 5/13
sin X = √ 1- cos²x
3) sin X = -12/13
⚆As sin functions-ve in 4th quadrant.
cosec X = 1/sin X
4) cosec X = -13/12
⚆As cosec functions-ve in 4th quadrant.
tan X = √ sec² x-1
5)tan X = -12/5
⚆As tan functions-ve in 4th quadrant.
Cot x = 1/ tan X
6)Cot x = -5/12
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Monika Gautam 5 years, 1 month ago
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