simplify tan^2 theta + 1/ tan^2 theta
csc2 theta
–1
~ tan2 theta ~
1
To simplify the expression tan^2 theta + 1/tan^2 theta, you can first simplify the denominator by rationalizing it.
The reciprocal of tan^2 theta is 1/tan^2 theta. To rationalize the denominator, multiply the numerator and denominator of the fraction by the conjugate of the denominator, which is tan^2 theta itself. This gives us:
1/tan^2 theta * tan^2 theta/tan^2 theta = tan^2 theta / (tan^2 theta)^2
Now, we can simplify the expression by combining like terms:
tan^2 theta / (tan^2 theta)^2 = tan^2 theta / (tan^4 theta)
Next, we can simplify the expression further by canceling out the common factors:
tan^2 theta / (tan^4 theta) = 1 / tan^2 theta
Therefore, the simplified expression is 1 / tan^2 theta.
Moving on to the expression "csc^2 theta":
The "csc" function is the reciprocal of the "sin" function. So, csc^2 theta is (1/sin theta)^2.
Squaring a fraction means squaring both the numerator and the denominator:
(1/sin theta)^2 = (1^2)/(sin^2 theta) = 1/(sin^2 theta)
Therefore, the expression "csc^2 theta" simplifies to 1/(sin^2 theta).
To summarize:
simplified expression of tan^2 theta + 1/tan^2 theta = 1 / tan^2 theta
simplified expression of csc^2 theta = 1/(sin^2 theta)