Question

If secA-tanA=4 then 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

Answer 2

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