Question

Use basic identities to simplify the expression.

cosecant of theta times cotangent of theta divided by secant of theta.

Answer 1

(csc*cot)/ sec

change everything into sin or cos and simplify

((1/sin)*(cos/sin))/ (1/cos)

=(cos/sin^2)/ (1/cos)

=(cos/sin^2) * (cos/1)

=cos^2/ sin^2

Answer 2

`cotg^(2) \theta`

Explanation:

The given expression is:

`(csc\theta (ctg\theta))/(sec\theta)`

But, we know that:

`csc\theta=(1)/(sin\theta)`

`ctg\theta = (cos\theta)/(sin\theta)`

`sec\theta=(1)/(cos\theta)`

Replacing all these basic identities in the given expression, we have:

`(csc\theta (ctg\theta))/(sec\theta)\\((1)/(sin\theta)(cos\theta)/(sin\theta))/((1)/(cos\theta))\\(cos^(2)\theta)/(sin^(2) \theta )\\((cos\theta)/(sin\theta))^(2)\\cotg^(2) \theta`