Solve cos a -sin a 1/cosa sina -1

Evaluate

cos (a) - sin (a) \times \frac{1}{cos ( a )} \times sin (a) - 1

Multiply

More Steps

cos (a) - \frac{sin ^{2} ( a )}{cos ( a )} - 1

Use sin^{2} t = 1 - cos^{2} t to transform the expression

cos (a) - \frac{1 - cos ^{2} ( a )}{cos ( a )} - 1

Subtract the terms

More Steps

\frac{2 cos ^{2} ( a ) - 1}{cos ( a )} - 1

Reduce fractions to a common denominator

\frac{2 cos ^{2} ( a ) - 1}{cos ( a )} - \frac{cos ( a )}{cos ( a )}

Write all numerators above the common denominator

\frac{2 cos ^{2} ( a ) - 1 - cos ( a )}{cos ( a )}

Transform the expression

2 cos (a) - \frac{1}{cos ( a )} - 1

Solution

2 cos (a) - sec (a) - 1

Simplify the expression