Verify the identity sec(beta) - 1 / cos(beta) = sec(beta)

1 − cos ( β ) sec ( β ) − 1 ​ = sec ( β )
we know that
sec ( β ) = cos ( β ) 1 ​
then, lets replace it
1 − cos ( β ) cos ( β ) 1 ​ − 1 ​ = cos ( β ) 1 ​
multiple each member by cos ( β )
1 − cos ( β ) 1 − cos ( β ) ​ = 1
simplifying
1 = 1

Answered by D3xt3R | 2024-06-10

To verify the given identity sec(beta) - 1 / cos(beta) = sec(beta), we need to manipulate the left side of the equation to match the right side. By simplifying the expression step by step and using trigonometric identities, we can show that the given equation is true.
To verify the given identity sec(beta) - 1 / cos(beta) = sec(beta), we need to manipulate the left side of the equation to match the right side .

Start by finding the common denominator of the fractions on the left side, which is cos(beta).
The expression becomes (sec(beta) - 1)/cos(beta).
Next, simplify the numerator: sec(beta) - 1 = (1/cos(beta)) - 1 = (1 - cos(beta))/cos(beta).
Substituting this back into the original expression, we have (1 - cos(beta))/cos(beta) / cos(beta).
Simplify further by multiplying the numerator and denominator by cos(beta) to get (1 - cos(beta))/(cos^2(beta)).
Using the identity sec^2(beta) = 1 + tan^2(beta), we rewrite cos^2(beta) = 1 - sin^2(beta) as 1/(1 - sin^2(beta)).
Therefore, (1 - cos(beta))/(cos^2(beta)) = (1 - cos(beta))/(1 - sin^2(beta)) = sec(beta).

Thus, we have verified that sec(beta) - 1 / cos(beta) = sec(beta).
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Answered by anuradhaborua | 2024-06-18

To verify the identity sec ( β ) − c o s ( β ) 1 ​ = sec ( β ) , we substitute sec ( β ) using its definition and simplify the expression. The identity confirms that both sides hold true in value, leading to the conclusion that the identity is verified. Therefore, the equation is indeed valid.
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Answered by D3xt3R | 2024-10-13