Question

54
11. If
If cosec2 (x/3/2) - cot2 (x+30/3)
=
cot 45°, then find the value of x.​

Answer 1

cosec

2

(

2

x

)−cot

2

(

3

x+30

)=cot45

\implies\,cosec^2(\frac{x}{2})-cot^2(\frac{x+30}{3})=1⟹cosec

2

(

2

x

)−cot

2

(

3

x+30

)=1

\implies\,cosec^2(\frac{x}{2})=1+cot^2(\frac{x+30}{3})⟹cosec

2

(

2

x

)=1+cot

2

(

3

x+30

)

\text{Using,}\boxed{\bf\,cosec^2A=1+cot^2A}Using,

cosec

2

A=1+cot

2

A

\implies\,cosec^2(\frac{x}{2})=cosec^2(\frac{x+30}{3})⟹cosec

2

(

2

x

)=cosec

2

(

3

x+30

)

\implies\,\frac{x}{2}=\frac{x+30}{3}⟹

2

x

=

3

x+30

\implies\,3x=2x+60⟹3x=2x+60

\implies\,3x-2x=60⟹3x−2x=60

\implies\,x=60⟹x=60

\therefore\textbf{The value of x is 60}∴The value of x is 60

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