Simplify:2sec^2A-2/4tan A...Please help,anyone who can answer
Should there be parentheses around 2sec^2A-2 in the numerator?
Yes, the question should be : 2(sec^A -2)/4 tan A
To simplify the given expression, let's break it down step by step.
Step 1: Simplify the numerator.
The numerator of the expression is 2sec^2A - 2. Since sec^2A is the reciprocal of cos^2A, we can rewrite it as:
2/cos^2A - 2
Step 2: Simplify the denominator.
The denominator of the expression is 4tan A. Recall that tan A is the ratio of sin A to cos A. So, we can rewrite it as:
4(sin A / cos A)
Step 3: Simplify further.
Now, let's combine the numerator and denominator:
(2/cos^2A - 2) / (4(sin A / cos A))
To simplify further, we can combine the terms in the numerator:
(2 - 2cos^2A) / (4(sin A / cos A))
Step 4: Simplify the numerator once more.
We can factor out a common factor of 2 in the numerator:
2(1 - cos^2A) / (4(sin A / cos A))
Since cos^2A + sin^2A = 1, the numerator becomes:
2(sin^2A) / (4(sin A / cos A))
Step 5: Simplify the expression.
Simplifying further, we can cancel out the common factor of 2 in the numerator and denominator:
sin^2A / (2(sin A / cos A))
Now, we can simplify the expression by dividing sin^2A by sin A and multiplying by cos A:
(sin A * cos A) / (2(sin A / cos A))
Step 6: Simplify the expression one last time.
Finally, cancel out the common factor of sin A in the numerator and denominator:
cos A / 2
Therefore, the simplified form of the expression 2sec^2A - 2/4tan A is cos A / 2.