Express cos theta and tan theta in terms of cosec theta
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Answer:
cos theta = √ (cosec²theta – 1)
cosec theta
tan theta = 1 ÷ √(cosec²theta – 1)
Step-by-step explanation:
cos theta
= √ (1 – sin²theta)
= √ {1 – (1 / cosec²theta)}
= √ {(cosec²theta – 1) / cosec²theta}
= √ (cosec²theta – 1) / cosec theta.
tan theta
= sin theta / cos theta
= (1 / cosec theta) / √(cosec²theta – 1) / cosec theta
= 1 / √ (cosec²theta – 1)
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