Question

Express cosecant theta in terms of cos theta ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Concept:

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

cosθ=1/secθ

sinA= perpendicular/hypotenuse

cosA=base/hypotenuse

tanA=perpendicular/base

cotA=1/tanA=base/perpendicular

secA=1/cosA= hypotenuse/base

cosecA=1/sinA=hypotenuse/perpendicular

Given:

cosecθ

Find:

Express cosecant theta in terms of cos theta

Solution:

We know,

cosθ=1/secθ

But it can be rewritten as ,

cosθ=cotθxsinθ

        =cotθ/cosecθ

but, cot²θ=cosec²θ-1

      ⇒cotθ=√(cosec²θ-1)

So, cosθ=√(cosec²θ-1)/cosecθ

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