Answer:
The given equation is sec(beta)-1/sec(beta)+1 = (1-cos(beta))/(1+cos(beta))
To prove this equation, we will start with the left-hand side (LHS) and simplify it to get the right-hand side (RHS).
LHS: sec(beta)-1/sec(beta)+1
We know that sec(beta) = 1/cos(beta). So we can substitute this value to get:
= (1/cos(beta)) - 1 / (1/cos(beta) + 1)
= (1/cos(beta)) - (cos(beta)/(cos(beta) + 1)) / ((cos(beta) + 1)/cos(beta))
= (1 - cos(beta))/(1 + cos(beta))
= RHS
Therefore, we have proved that sec(beta)-1/sec(beta)+1 = (1-cos(beta))/(1+cos(beta)).
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Answers & Comments
Answer:
The given equation is sec(beta)-1/sec(beta)+1 = (1-cos(beta))/(1+cos(beta))
To prove this equation, we will start with the left-hand side (LHS) and simplify it to get the right-hand side (RHS).
LHS: sec(beta)-1/sec(beta)+1
We know that sec(beta) = 1/cos(beta). So we can substitute this value to get:
= (1/cos(beta)) - 1 / (1/cos(beta) + 1)
= (1/cos(beta)) - (cos(beta)/(cos(beta) + 1)) / ((cos(beta) + 1)/cos(beta))
= (1 - cos(beta))/(1 + cos(beta))
= RHS
Therefore, we have proved that sec(beta)-1/sec(beta)+1 = (1-cos(beta))/(1+cos(beta)).