Question 62

If $$\sin \theta + \cosec \theta = 2$$, then what is the value of $$\sin^{153} \theta + \cosec^{253} \theta$$ ?

Solution

$$\sin \theta + \cosec \theta = 2$$

$$\sin \theta +\frac{1}{\sin \theta} = 2$$

Let $$\sin \theta = x$$

$$x+\frac{1}{x} = 2$$

If sum of a number and its reciprocal is 2 then number will be 1

So, $$\sin \theta = 1$$

$$\sin^{153} \theta + \cosec^{253} \theta$$ = $$1^{153}+1^{253}=2$$

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