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Sec A + Tan A = 3 => Sec A =1) 10/3 2) 5/3 3) 2/3 4) 4/3

Sec A + Tan A = 3 => Sec A =1) 10/3 2) 5/3 3) 2/3 4) 4/3

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Grade:8

1 Answers

manna
59 Points
4 years ago
secA+tanA=3
1/cosA+sinA/cosA=3
1+sinA/cosA=3
1+sinA=3*cosA
1+sinA=3(I'll rewrite cos%28A%29 as sqrt%281-sin%5E2%28A%29%29 

sin%28A%29+%2B+1+=+3sqrt%281+-+sin%5E2+%28A%29%29
Squaring both sides, 

sin%5E2+%28A%29+%2B+2sin%28A%29+%2B+1+=+9+-+9+sin%5E2+%28A%29 Let u=sinA. It is easy to see that we can now obtain a quadratic: 

10u%5E2+%2B+2u+-+8+=+0 --> 5u%5E2+%2B+u+-+4+=+0
u+=+%28-1+%2B-+sqrt%281+%2B+80%29%29%2F10+=+%28-1+%2B-+9%29%2F10 = -1 or 4/5.
sinA=4/5
cosA=3/5
sec=1/cos=5/3
 
answer is sec =5/3

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