SOLUTION: if tan A= √2 -1 so solve sin A.cos A = √2/4
ANSWER
Two things before we start: First, "solve" in the problem above should really read "prove"; Second, we are goin
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-> SOLUTION: if tan A= √2 -1 so solve sin A.cos A = √2/4
ANSWER
Two things before we start: First, "solve" in the problem above should really read "prove"; Second, we are goin
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Question 830914: if tan A= √2 -1 so solve sin A.cos A = √2/4
ANSWER
Two things before we start: First, "solve" in the problem above should really read "prove"; Second, we are going to use r2 for the square root of 2 (we are not trying to complicate the problem, just using a symbol that can be read on all computers). Now let us start:
1. tan A = r2 - 1
2. sin A = (tan A)(cos A)
3. So (sin A)(cos A) = (tan A)(cos A)(cos A) = (tan A)(cos A)^2
4. But cos A = 1/(sec A) so the above can be written as (tan A)/(sec A)^2
5. Also (sec A)^2 = 1 + (tan A)^2 so we now have (tan A)/[1 + (tan A)^2]
6. If we substitute for tan A we will get (r2 - 1)/[1 + (r2 - 1)^2]
7. Working on the denominator (leaving the numerator alone for now)
yields (r2 - )/(1 + 2 + 1 - 2r2) = (r2 -1)/(4 - 2r2)
8. Now multiply both numerator and denominator by (r2 + 1) to give
(r2 - 1)(r2 + 1)/[(4 - 2r2)(r2 + 1)]
9. The numerator amounts to 2 - 1 = 1
10. The denominator amounts to 4r2 - 4 + 4 - 2r2 = 2r2
11. So we now have 1/(2r2)
12. Now multiply both numerator and denominator by r2: We would get r2/4
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