1/sec(x)-tan(x) = sec(x) + tan(x) I need to verify the trigonometric identity pls
The way you typed it, it is not an identity, you must have meant:
1/(secx - tanx) = secx + tanx
LS = 1/(secx - tanx) *(secx + tanx)/(secx + tanx)
= (secx + tanx)/(sec^2 x - tan^2 x) , but tan^2 x = sec^2 - 1
= (secx + tanx)(sec^2 x - (sec^2 x - 1) )
= (secx + tanx)/1
= RS
clear the fraction. You k ow that
sec^2x = 1 + tan^2x
To verify the trigonometric identity 1/sec(x) - tan(x) = sec(x) + tan(x), we will start with the left-hand side (LHS) of the equation and simplify it to see if it equals the right-hand side (RHS).
LHS: 1/sec(x) - tan(x)
Since sec(x) is equal to 1/cos(x), we can rewrite the LHS as follows:
LHS: 1/(1/cos(x)) - tan(x)
Now, we can simplify the expression further by taking the reciprocal of a fraction:
LHS: cos(x) - tan(x)
Next, we need to simplify the RHS of the equation to compare it with the simplified LHS.
RHS: sec(x) + tan(x)
Since sec(x) is equal to 1/cos(x), we can rewrite the RHS as follows:
RHS: 1/cos(x) + tan(x)
To combine these terms, we need a common denominator. The common denominator in this case is cos(x). So, we can rewrite the RHS as follows:
RHS: (1 + cos(x) * tan(x))/cos(x)
Now, we can simplify the expression further by distributing cos(x) into the numerator:
RHS: (cos(x) + sin(x))/cos(x)
Since cos(x)/cos(x) is equal to 1, we can simplify the expression further:
RHS: 1 + sin(x)/cos(x)
And since sin(x)/cos(x) is equal to tan(x), we can further simplify:
RHS: 1 + tan(x)
Now, we can see that the simplified RHS is equal to the simplified LHS:
LHS: cos(x) - tan(x)
RHS: 1 + tan(x)
Both expressions are equal, which verifies the trigonometric identity 1/sec(x) - tan(x) = sec(x) + tan(x).