can you solve this problem
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it is a alegabric equation
chiragpc:
algebraic and trigonometry
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Answer:
a - 1/a = ±4
a³ - 1/a³ = ±76
Step-by-step explanation:
Write k = a - 1/a.
Then k² = a² - 2(a)(1/a) + 1/a² = a² + 1/a² - 2 = 18 - 2 = 16.
So k = 4 or k = -4.
Cubing k, we have
k³ = ( a - 1/a )³
= a³ - 3 a² (1/a) + 3 a (1/a)² - 1/a³
= a³ - 3a + 3/a - 1/a³
= a³ - 1/a³ - 3 ( a - 1/a )
= a³ - 1/a³ - 3 k
Hence
a³ - 1/a³ = k³ + 3k = ± ( 64 + 12 ) = ±76.
It's not clear to me what's meant in the trigonometric exercise. It looks like it's just asking for tan 30 times tan 60. Well, the angles add up to 90 degrees, so the product is just 1.
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?of what? In general, if x + y = 90 degrees, then tan(x) tan(y) = 1. You can see this by drawing a right angled triangle. The side opposite the angle x is the side adjacent to angle y, and vice versa, so tan(x) = 1 / tan(y) and the product of the tans is 1.
answer
The answer is just " 1 ".
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