When csc(theta) sin(theta) is simplified, what is the result?
2 answers:
Cosec theta = 1/sin theta
<span>Therefore, csc theta * sin theta = 1. </span>
<span>cosec theta = 1/sin theta, sec theta = 1 / cos theta. </span>
<span>Therefore, Equation 2 reduces to, </span>
<span>(1/sin theta) / (1/cos theta) = cos theta/sin theta = 1/tan theta = cot theta. </span>
<span>tan theta + cot theta = tan theta + 1/tan theta. Taking LCM, </span>
<span>= (1 + tan^2 theta)/tan theta </span>
<span>From the identities, 1 + tan^2 theta = sec^2 theta. </span>
<span>Hence, equation 3 reduces to, </span>
<span>sec^2 theta/tan theta = (1/cos^2 theta) / (sin theta/cos theta) </span>
<span>= cos theta / (sin theta * cos^2 theta) </span>
<span>= 1 / (sin theta*cos theta). This cannot be reduced, hence is equal to sec theta*cosec theta. </span>
<span>1-sin^2 theta / 1+sin theta = (1 + sin theta)*(1-sin theta) / (1 + sin theta) </span>
<span>= 1 - sin theta. </span>
<span>Hope this helped :)</span>
Answer:
Answer is 1
Edgen answer is D
Step-by-step explanation:
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