Question

The angle A is such that
secA + tanA = 2
Show that
secA-tanA=1/2
Hence, find the exact value of cosA.

Answer 1

use (secA + tanA )(secA-tanA)=1
thus secA-tanA=1/2

Answer 2

Solve simultaneously
2secA=5/2
cosA=4/5

Answer 3

Don't really understand... Can you start from the beginning?

Answer 4

You get the first part? right
\[\sec^2A-\tan^2A=1=(secA-tanA)(secA+tanA)\]

Answer 5

Not the "thus secA-tanA=1/2"

Answer 6

Use result from first part with what is already given and add the two
\[(secA+tanA)+(secA-tanA)=2+1/2\]

Answer 7

\[\sec A + \tan A = \frac 1{(\sec A - \tan A)} \]

Answer 8

Oh Ok.

Answer 9

Note \(A \neq n\pi + \frac{\pi}{2} \) and \(n \in \mathbb{z} \)

Answer 10

Ok, so how do you get the second part of the answer? @NotSObright and @FoolForMath

Answer 11

Add the two equation.

Answer 12

Already mentioned

Answer 13

order order think think :)

Answer 14

But how did you get this in the first place?
2secA=5/2
cosA=4/5

I'm trying!... I'm trying!.... It's difficult for me though.. :/

Answer 15

sec A = 1/ cos A

Answer 16

Still lost... :( My brain isn't working well today...