Question

if sec A - tan A=4 prove that cosA= 8/17​

Answer 1

Sec A -tan A =4..(i)

Also, sec ^2 A-tan ^2 A=1. (identity)

=>(sec A+tan A)(sec A-tan A)= 1

=>(sec A+tan A)=1/4..(ii)

Adding eq (I) and (ii)

2sec A=(4+1/4)=17/4

=>sec A =17/8

=>Cos A =1/sec A=8/17.

Hence,proved

Hope it helps

                      or another method

secA-tanA=4

squaring both sides

(secA-tanA) ²=4²

sec²A+tan²A-2secAtanA=16

sec²A+sec²A-1-2secAtanA=16

2sec²A-2secAtanA=16+1

2secA(secA-tanA) =17 -------(given)

2secA(4)=17

8secA=17

secA=17/8

1/cosA=17/8

cosA=8/17

hence proved