Solve 1/sec a-tan a - 1/cosa

Question

Simplify the expression

- tan (a) sin (a) - tan (a)

Evaluate

\frac{1}{sec ( a )} - tan (a) - \frac{1}{cos ( a )}

Subtract the terms

More Steps

\frac{cos ( a ) - sec ( a )}{sec ( a ) cos ( a )} - tan (a)

Reduce fractions to a common denominator

\frac{cos ( a ) - sec ( a )}{sec ( a ) cos ( a )} - \frac{tan ( a ) sec ( a ) cos ( a )}{sec ( a ) cos ( a )}

Write all numerators above the common denominator

\frac{cos ( a ) - sec ( a ) - tan ( a ) sec ( a ) cos ( a )}{sec ( a ) cos ( a )}

Transform the expression

More Steps

\frac{\frac{c o s ^{2} ( a ) - 1 - t a n ( a ) c o s ( a )}{c o s ( a )}}{sec ( a ) cos ( a )}

Transform the expression

More Steps

\frac{\frac{c o s ^{2} ( a ) - 1 - t a n ( a ) c o s ( a )}{c o s ( a )}}{1}

Divide the terms

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

Transform the expression

More Steps

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

Transform the expression

More Steps

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

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

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

Transform the expression

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

Use \frac{sin ( t )}{cos ( t )} = tan (t) to transform the expression

- (sin (a) + 1) tan (a)

Calculate

(- sin (a) - 1) tan (a)

Solution

- tan (a) sin (a) - tan (a)

Show Solution