Hi, can someone give me the answer to this 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.

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

cos A= 4(12/17)

Cos A= 48/17

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

To solve the equation secA - tanA = 1/4, we'll use the trigonometric identity:

secA = 1/cosA, and tanA = sinA/cosA.

So, substituting these values into the equation, we have:

1/cosA - sinA/cosA = 1/4.

To simplify the equation, we need a common denominator. The common denominator here is cosA.

So, the equation becomes:

(1 - sinA) / cosA = 1/4.

Next, we can cross-multiply to get rid of the fractions:

4(1 - sinA) = cosA.

This is equivalent to the equation you obtained:

cosA = 4(1 - sinA).

To determine if your answer is correct, let's compare it to the equation we just derived.

To further solve for cosA, we need to eliminate the sinA term. We'll expand the expression:

4 - 4sinA = cosA.

Now, let's solve for sinA.

To do this, we'll isolate the sinA term:

4sinA = 4 - cosA.

Divide both sides by 4 to solve for sinA:

sinA = (4 - cosA) / 4.

Now that you have sinA, we can substitute this expression back into the original equation you obtained:

cosA = 4(1 - sinA).

Replacing sinA with (4 - cosA) / 4:

cosA = 4(1 - (4 - cosA) / 4).

Simplifying further:
cosA = 4 - (4 - cosA)
cosA = 4 - 4 + cosA
cosA = cosA.

The equation evaluates to cosA = cosA, which is always true.

Therefore, your answer, cosA = 4(1 - sinA), is valid.