Answered

Use basic identities to simplify the expression.


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

Verified Answer :

Jim4109

(csccot)/ 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:

\(cotg^{2} \theta\)

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:

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

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