if sinA+cosA=1/5 then tanA is
Answers
Step-by-step explanation:
if sinA+cosA=1/5, then a value of tanA/2 satisfies which of the equation?
a. 2x^2-x-1
b.x^2-2x-3=0
c.2x^2-5x-3=0
d. 2x^3-7x^2+2x+3=0
shreya
May 30, 2011
sinA+cosA=1/5
square both sides
sin^2A + 2sinAcosA + cos^2A = 1/25
2sinAcosA = 1/25 - 1 = -24/25
sin 2A = -24/25
setting my calculator to radians
2A = 4.4286 or 2A = 4.9962
A/2 = 1.10715 or A/2 = 1.249
so tan A/2 = 3.99999 or tan A/2 = 3
or tan A/2 = 0
clearly 0 does not work as a zero for any of the given equations, (they all have a constant)
tan A/2 = 3 does work in equation b)
which would factor to (x-3)(x+1) = 0 to get a root of 3
3 is also a root of c) and d) since they both factor containing a factor of (x-3)
( I know I should have been able to get tan A/2 = 3 without relying on my calculator,
Answer:
-4/3
Step-by-step explanation:
→ 1 + tanA = 1/5 (dividing both sides with cos)
→ 25 + 50tanA + 25tan²A = sec²A (squaring both sides)
→ solving tan A = -3/4 or tan A = -4/3
→ tan A -4 → cos A + sin A = -1/5
Hence , tan A = -4/3