Question

cosy/1-siny = 1+siny/cosy
varify using trig identity.

Answer 1

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

$\displaystyle \frac{\cos y}{1-\sin y}=\frac{1+\sin y}{\cos y}$

On the left, we can multiply both layers by (1 + sin(y)):

$\displaystyle \frac{\cos y}{1-\sin y}\left(\frac{1+\sin y}{1+\sin y}\right)=\frac{1+\sin y}{\cos y}$

Multiply:

$\displaystyle \frac{\cos y(1+\sin y)}{1-\sin^2 y}=\frac{1+\sin y}{\cos y}$

From the Pythagorean Theorem, we know that sin²(y) + cos²(y) = 1. Hence, 1 - sin²(y) = cos²(y). Substitute:

$\displaystyle \frac{\cos y(1+\sin y))}{\cos^2 y}=\frac{1+\sin y}{\cos y}$

Cancel:

$\displaystyle \frac{1+\sin y}{\cos y}=\frac{1+\sin y}{\cos y}$

Hence proven.