Flag Trigonometry> Sec A + Tan A = 3 => Sec A =1) 10/3 2) 5/...
question mark

Sec A + Tan A = 3 => Sec A=1) 10/32) 5/33) 2/3 4) 4/3

Vyanktesh Kulkarni , 7 Years ago
Grade 8
anser 1 Answers
manna

Last Activity: 7 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

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...