Tanα-secα+1/tanα+secα-1. Please. Give. Me. Ans...
1 / tan α = cot α
- sec α + sec α = 0
So:
tan α - sec α + 1 / tan α + sec α - 1 = tan α + cot α - 1
What is your question?
To simplify the expression tanα - secα + 1 / tanα + secα - 1, we can combine like terms and find a common denominator.
First, let's simplify the numerator:
tanα - secα + 1 = (sinα / cosα) - (1 / cosα) + 1 = (sinα - 1 + cosα) / cosα
And now, let's simplify the denominator:
tanα + secα - 1 = (sinα / cosα) + (1 / cosα) - 1 = (sinα + 1 - cosα) / cosα
Now, we can combine the simplified numerator and denominator:
((sinα - 1 + cosα) / cosα) / ((sinα + 1 - cosα) / cosα)
Next, we can simplify by multiplying the numerator by the reciprocal of the denominator:
((sinα - 1 + cosα) / cosα) * (cosα / (sinα + 1 - cosα))
Now, we can simplify further by canceling out common terms:
sinα - 1 + cosα / sinα + 1 - cosα
Therefore, the simplified expression is (sinα - 1 + cosα) / (sinα + 1 - cosα).
To simplify the expression Tanα-secα+1/tanα+secα-1, you may follow these steps:
Step 1: Identify a common denominator for the two fractions within the expression. In this case, the common denominator is (tanα + secα - 1)(tanα + secα + 1).
Step 2: Arrange the terms within the numerator with respect to the common denominator. The expression can be written as (tanα(tanα + secα + 1) - (secα - 1))/(tanα + secα + 1).
Step 3: Expand and simplify the numerator. Distribute tanα to the terms within the parentheses to obtain tan^2α + tanα(secα + 1) - secα + 1.
Step 4: Combine like terms in the numerator. Group the terms that have a similar power of tanα to get (tan^2α + tanα) + (tanα(secα - 1) + 1 - secα).
Step 5: Further simplify the expression. We know that tan^2α + tanα is equal to tanα(tanα + 1). Thus, the expression can be written as tanα(tanα + 1) + (tanα(secα - 1) + 1 - secα).
Therefore, the simplified expression is tanα(tanα + 1) + (tanα(secα - 1) + 1 - secα).