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 ->  Sequences-and-series -> 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 ) (      Log On


   

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) About Me  (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 _______ . 
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4tan%28alpha%29+%2B+3cot%28alpha%29+=7

Use cot%28theta%29=1%2Ftan%28theta%29

4tan%28alpha%29+%2B+3%281%2Ftan%28alpha%29%29+=7

Multiply through by tan%28alpha%29

4tan%5E2%28alpha%29+%2B+3+=7tan%28alpha%29

4tan%5E2%28alpha%29+-7tan%28alpha%29%2B3=0

Factor:

%284tan%28alpha%29-3%29%28tan%28alpha%29-1%29=0

4tan%28alpha%29=3;   tan%28alpha%29=1
                  alpha=cross%28pi%2F4%29      

tan%28alpha%29=3%2F4

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

                                  

sin%28alpha%29=3%2F5, cos%28alpha%29=4%2F5

sin%282alpha%29=2sin%28alpha%29cos%28alpha%29
sin%282alpha%29=2%283%2F5%29%284%2F5%29
sin%282alpha%29=24%2F25

Correct answer is (d)

Edwin