Question

If tanA + secA = 3 prove 5sinA = 4

Answer 1

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Answer 2

Answer:

Hope, it will help you!

Step-by-step explanation:

tanA+secA=3

sinA/cosA + 1/cosA =3

sinA+1/cosA = 3

sinA+1= 3 cosA

( squaring on both sides),

  (sinA+1)^2 = (3 cos A)^2

sin^2A + 2sinA + 1 = 9 cos^2 A

sin^2A + 2sinA + 1= 9(1-sin^2A)

sin^2A + 2sinA + 1= 9- 9 sin^2A

sin^2A+ 9 sin^2A + 10 sinA- 8sinA + 1-9 = 0

10sin^2A + 10 sinA- 8sinA + -8 = 0

10sinA(sinA+1) -8 (sinA+1)=0

(sinA+1) (10sinA-8) = 0

EITHER,

sinA+1 = 0

sinA = (-1)

OR,

10sinA-8=0

10sinA=8

sinA= 8/10

sinA=4/5

5sinA=4            proved!