Exercise
$\frac{1+\cos\left(a\right)+\sin\left(a\right)}{1+\cos\left(a\right)-\sin\left(a\right)}$
Step-by-step Solution
Learn how to solve special products problems step by step online. Simplify the trigonometric expression (1+cos(a)sin(a))/(1+cos(a)-sin(a)). Multiply and divide the fraction \frac{1+\cos\left(a\right)+\sin\left(a\right)}{1+\cos\left(a\right)-\sin\left(a\right)} by the conjugate of it's denominator 1+\cos\left(a\right)-\sin\left(a\right). Multiplying fractions \frac{1+\cos\left(a\right)+\sin\left(a\right)}{1+\cos\left(a\right)-\sin\left(a\right)} \times \frac{1+\cos\left(a\right)+\sin\left(a\right)}{1+\cos\left(a\right)+\sin\left(a\right)}. When multiplying two powers that have the same base (1+\cos\left(a\right)+\sin\left(a\right)), you can add the exponents. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2.
Simplify the trigonometric expression (1+cos(a)sin(a))/(1+cos(a)-sin(a))
Final answer to the exercise
$\frac{1+2\left(\cos\left(a\right)+\sin\left(a\right)\right)+\cos\left(a\right)^{2}+2\cos\left(a\right)\sin\left(a\right)+\sin\left(a\right)^{2}}{\left(\cos\left(a\right)+1\right)^2-\sin\left(a\right)^2}$