SOLUTION: If α is an acute angle and 4tanα + 3cotα =7 , where α≠π/4 then the vlue of 2α is _______ . (a) π (b) Sin^(-1)(7/√50 ) (

Algebra.Com
Question 974457: If α is an acute angle and 4tanα + 3cotα =7 , where α≠π/4 then the vlue of 2α is _______ .
(a) π
(b) Sin^(-1)(7/√50 )
(c) Sin^(-1)(7/25)
(d) Sin^(-1)(24/25)
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
f α is an acute angle and 4tanα + 3cotα =7 , where α≠π/4 then the vlue of 2α is _______ . 
-------------------



Use 



Multiply through by 





Factor:



;   
                        



Draw a right triangle with opposite=3 and adjacent = 4, so
a will have tangent 3/4. Use Pythagorean
theorem to find hypotenuse 5.

                                  

, 





Correct answer is (d)

Edwin
RELATED QUESTIONS

Given that tan α=p, where α is acute, find in terms of p, tan(−α),... (answered by stanbon)
If sin α = ½ and α is acute, then (3cosα- 4 cos²α) = ? (a.) 0 (b.) (answered by brysca)
If tan α = 9 and α is acute, find the exact value of sin... (answered by tommyt3rd)
Use the given information to find the values of sin α/2 , cos α/2 , tan... (answered by stanbon)
Let α & β be acute angles such that tan α=7 and sin β=4/5. Prove that (answered by lwsshak3)
If α+β=π/3 the and sin α=1/2 then find the value of sinβ what... (answered by stanbon)
What is the value of cos(2α) , if sin(3α) =2... (answered by MathLover1,ikleyn)
α=1/7π rad. Angle θ is such that π2<θ<2π and... (answered by ikleyn)
What is the value of sin α if tan α = -5/9 and sec α > 0? (answered by jim_thompson5910)