cosx/(1+secx)
Please help me simplify this expression.
cosx/(1+1/cosx)
= cosx/( (cosx + 1)/cosx )
= cosx * cosx/(cox + 1)
= cos^2x /(cosx + 1)
Not much of a simplification , I would say the original is more "simplified"
Thank you!
To simplify the expression cosx/(1+secx), we can apply a common trigonometric identity.
Recall that secx is equal to 1/cosx. So we can substitute 1/cosx for secx in the expression:
cosx/(1+1/cosx)
Next, to add the fractions in the denominator, we need to find the common denominator. The common denominator in this case is cosx. So we can rewrite the expression as:
cosx/(cosx/cosx + 1/cosx)
Now, simplify the fractions in the denominator:
cosx/((1 + cosx)/cosx)
Next, to divide by a fraction, we multiply by the reciprocal:
cosx * (cosx/(1 + cosx))
Finally, we can cancel out the cosx terms:
(cosx * cosx)/(1 + cosx)
Simplifying further, we have:
cos^2(x)/(1 + cosx)
And there you have it. The simplified expression is cos^2(x)/(1 + cosx).