what are the steps to solve sec y sin (pi/2-y)=1
Use the identities
sin(π/2-x)=cos(x)
and
sec(x)=1/cos(x)
to transform the equation in terms of cos(x), which will then show that the "equation" is in fact an identity, i.e. it is true for all values of x.
To solve the equation sec(y)sin(pi/2 - y) = 1, follow these steps:
Step 1: Simplify the equation using trigonometric identities.
- Since sec(x) is the reciprocal of cos(x), we can rewrite it as 1/cos(y). Similarly, sin(pi/2 - y) can be written as cos(y). The equation becomes (1/cos(y)) * cos(y) = 1.
Step 2: Cancel out common terms.
- In the simplified equation, the cos(y) terms cancel each other out. This leaves us with 1 = 1.
Step 3: Analyze the result.
- Since 1 = 1 is always true, this means that the original equation is true for any value of y.
Therefore, there is no specific solution for the equation sec(y)sin(pi/2 - y) = 1. It holds true for all values of y.
To solve the equation sec(y) sin(pi/2 - y) = 1, follow these steps:
Step 1: Simplify the equation using trigonometric identities:
a) Rewrite sec(y) as 1/cos(y).
b) Rewrite sin(pi/2 - y) as cos(y).
The equation becomes:
1/cos(y) * cos(y) = 1
Cos(y) cancels out, leaving you with: 1 = 1.
Step 2: Analyze the simplified equation, 1 = 1.
Since 1 is always equal to 1, the equation is true for all y.
Step 3: Interpret the solution.
The solution to the equation is all real numbers y.
Therefore, the steps to solve sec(y) sin(pi/2 - y) = 1 are:
Step 1: Simplify the equation.
Step 2: Analyze the simplified equation.
Step 3: Interpret the solution.