Please help me to simplify using identities
1+tan^2x/tan^2x
I don't really understand how to do please help
the way you typed it:
1+tan^2x/tan^2x
= 1 + 1
= 2
what you probably meant:
(1+tan^2x)/tan^2x
= sec^2 x / tan^2 x
= (1/cos^2 x) / (sin^2 x/cos^2 x)
= 1/sin^2 x
or
= csc^2 x
(1+tan^2x)/tan^2x
= 1/tan^2x + 1
= cot^2x + 1
= csc^2x
To simplify the expression 1 + tan^2(x) / tan^2(x), we can use the trigonometric identity known as the Pythagorean identity. The Pythagorean identity states that for any angle x, sin^2(x) + cos^2(x) = 1.
Now, let's substitute tan^2(x) with its equivalent form using the Pythagorean identity.
Recall that tan(x) = sin(x) / cos(x).
So, we can rewrite tan^2(x) as sin^2(x) / cos^2 (x).
Now let's simplify the original expression:
1 + tan^2(x) / tan^2(x)
= 1 + (sin^2(x) / cos^2(x)) / (sin^2(x) / cos^2(x))
To divide fractions, we can multiply the first fraction by the reciprocal (or multiplicative inverse) of the second fraction.
= 1 + (sin^2(x) / cos^2(x)) * (cos^2(x) / sin^2(x))
Next, we can cancel out the common factors:
= 1 + (sin^2(x) * cos^2(x)) / (cos^2(x) * sin^2(x))
Since the numerator and denominator have the same terms, we can further simplify:
= 1 + 1
= 2
Therefore, the simplified form of 1 + tan^2(x) / tan^2(x) is 2.