5411. IfIf cosec2 (x/3/2) – cot2 (x+30/3)= cot 45°, then find the value of x. About the author Camila
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 Find more: If log tan A+log tan B=0 then find log sin(A+B) where A and B are acute angles Reply
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
Find more:
If log tan A+log tan B=0 then find log sin(A+B) where A and B are acute angles