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
Algebra.Com
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
Answer by Elomeht(22) (Show Source): You can put this solution on YOUR website!
RELATED QUESTIONS
Here is my problem.
[SQRT(x + 7)] - 2[SQRT(x)] =-2
OR
√(x + 7) -... (answered by lwsshak3)
I'm kinda stuck on these three identity Questions: Could you explain how to solve these... (answered by Alan3354,nyc_function)
How to solve it:
4 sin 5Pi/12 cos 5pi/12 = ?
Answers:
a ) √ 2
b) 1
c)... (answered by lwsshak3)
Please help me solve this problem!
If we establish an identity, -sin A csc A - sin^2 A - (answered by jojo14344)
1) Solve the following equations.
a) √X - 1= 3
Answer:
Show work in this... (answered by pradhyumna.kumar@gmail.com)
Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u= 4/5 where... (answered by Fombitz)
Need help!!!! Find the exact value of sin 2u, cos 2u, sin u/2, and cos u/2 give: cos u=... (answered by lwsshak3)
Just not getting this.
Suppose cos t = -0.4 and csc t < 0 . Find each of the following (answered by lwsshak3)
Solve for a. 2√a-1 = 4√a
If you could show every step I would appreciate... (answered by solver91311)