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

Answer:

$cotg^{2} \theta$

Step-by-step explanation:

The given expression is:

$\frac{csc\theta (ctg\theta)}{sec\theta}$

But, we know that:

$csc\theta=\frac{1}{sin\theta}$

$ctg\theta = \frac{cos\theta}{sin\theta}$

$sec\theta=\frac{1}{cos\theta}$

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

$\frac{csc\theta (ctg\theta)}{sec\theta}\\\frac{\frac{1}{sin\theta}\frac{cos\theta}{sin\theta}}{\frac{1}{cos\theta}}\\\frac{cos^{2}\theta}{sin^{2} \theta }\\(\frac{cos\theta}{sin\theta})^{2}\\cotg^{2} \theta$