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Question

If 3x=cosec θ and 3x=cot θ, find the value of  3(x21x2).


Solution

Use A in place of theta

3x=cosecA

x=cosecA3

x2=cosec2A9...... (i)

3x=cotA

1x=cotA3

1x2=cot2A9...........(ii)

3(x21x2)=3(cosec2A9cot2A9)

=3(cosec2Acot2A9)

=3(19)

=3×19=13

So answer is 3(x21x2)=13.

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