Hi, can someone give me the answer to this question:

Question

secA-tanA=1/4. Find cosA

I got: CosA=4(1-sinA) Is my answer good?



Now multply each side by (1+sinA)
CosA(1+sinA)=4 cos^2 A
CosA=1/4 (1+sinA)

16(1-sinA)=1+sinA
15=17SinA
So you have sinA, now find Cos A from your equation you originally solved.

Answer 1

Cos A= 4(1-(15/17))

cos A= 4(12/17)

Cos A= 48/17

Answer 2

SecA+ tanA ans secA-tanA are reciprocals of each other as their product is 1.
So secA-tanA = 1/4 means secA+tanA=4 adding, 2secA=17/4 so secA= 17/8 or cosA=8/17