\[~\left( \mathbf{iii} \right)~tan\text{ }3x\text{ }+\text{ }tan\text{ }x\text{ }=\text{ }2\text{ }tan\text{ }2x\] Or, \[tan\text{ }3x\text{ }+\text{ }tan\text{ }x\text{ }=\text{ }2\text{ }tan\text{...
Solve the following equations: (i) tan x + tan 2x + tan 3x = 0 (ii) tan x + tan 2x = tan 3x
The general solution of any trigonometric equation is given as: \[sin\text{ }x\text{ }=\text{ }sin\text{ }y,\] or \[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{n~}}y,\]...
Solve the following equations: (ix) sin 2x – sin 4x + sin 6x = 0
\[\left( \mathbf{ix} \right)~sin\text{ }2x\text{ }\text{ }sin\text{ }4x\text{ }+\text{ }sin\text{ }6x\text{ }=\text{ }0\] Or, \[sin\text{ }2x\text{ }\text{ }sin\text{ }4x\text{ }+\text{...
Solve the following equations: (vii) sin x + sin 2x + sin 3x + sin 4x = 0 (viii) sin 3x – sin x = 4 cos2 x – 2
\[~\left( \mathbf{vii} \right)~sin\text{ }x\text{ }+\text{ }sin\text{ }2x\text{ }+\text{ }sin\text{ }3x\text{ }+\text{ }sin\text{ }4x\text{ }=\text{ }0\] Or, \[sin\text{ }x\text{ }+\text{ }sin\text{...
Solve the following equations: (v) cos x + sin x = cos 2x + sin 2x (vi) sin x + sin 2x + sin 3x = 0
\[~\left( \mathbf{v} \right)~cos\text{ }x\text{ }+\text{ }sin\text{ }x\text{ }=\text{ }cos\text{ }2x\text{ }+\text{ }sin\text{ }2x\] Or, \[cos\text{ }x\text{ }+\text{ }sin\text{ }x\text{ }=\text{...
Solve the following equations: (iii) sin x + sin 5x = sin 3x (iv) cos x cos 2x cos 3x = 1/4
\[\left( \mathbf{iii} \right)~sin\text{ }x\text{ }+\text{ }sin\text{ }5x\text{ }=\text{ }sin\text{ }3x\] Or, \[sin\text{ }x\text{ }+\text{ }sin\text{ }5x\text{ }=\text{ }sin\text{ }3x\] \[sin\text{...
Solve the following equations: (i) cos x + cos 2x + cos 3x = 0 (ii) cos x + cos 3x – cos 2x = 0
The general solution of any trigonometric equation is given as: \[sin\text{ }x\text{ }=\text{ }sin\text{ }y,\] or, \[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{n~}}y,\]...
Solve the following equation: (vii) cos 4x = cos 2x
\[~\left( \mathbf{vii} \right)~cos\text{ }4x\text{ }=\text{ }cos\text{ }2x\] Or, \[cos\text{ }4x\text{ }=\text{ }cos\text{ }2x\] \[4x\text{ }=\text{ }2n\pi \text{ }\pm \text{ }2x\] So, \[4x\text{...
Solve the following equations: (v) tan2 x + (1 – √3) tan x – √3 = 0 (vi) 3 cos2 x – 2√3 sin x cos x – 3 sin2 x = 0
\[~\left( \mathbf{v} \right)~ta{{n}^{2}}~x\text{ }+\text{ }\left( 1\text{ }\text{ }\surd 3 \right)\text{ }tan\text{ }x\text{ }\text{ }\surd 3\text{ }=\text{ }0\] Or, \[ta{{n}^{2}}~x\text{ }+\text{...
Solve the following equations: (iii) 2 sin2 x + √3 cos x + 1 = 0 (iv) 4 sin2 x – 8 cos x + 1 = 0
\[\left( \mathbf{iii} \right)~2\text{ }si{{n}^{2}}~x\text{ }+\text{ }\surd 3\text{ }cos\text{ }x\text{ }+\text{ }1\text{ }=\text{ }0\] Or, \[2\text{ }si{{n}^{2}}~x\text{ }+\text{ }\surd 3\text{...
Solve the following equations: (i) sin2 x – cos x = 1/4 (ii) 2 cos2 x – 5 cos x + 2 = 0
According to any general solution of trigonometric equation , \[sin\text{ }x\text{ }=\text{ }sin\text{ }y,\] or, \[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{n~}}y\] ,...
Find the general solutions of the following equations: (xi) sin x = tan x (xii) sin 3x + cos 2x = 0
(xi) \[sin\text{ }x\text{ }=\text{ }tan\text{ }x\] Or, \[sin\text{ }x\text{ }=\text{ }tan\text{ }x\] \[sin\text{ }x\text{ }=\text{ }sin\text{ }x/cos\text{ }x\] or, \[sin\text{ }x\text{ }cos\text{...
Find the general solutions of the following equations: (ix) tan px = cot qx (x) sin 2x + cos x = 0
\[\left( \mathbf{ix} \right)~tan\text{ }px\text{ }=\text{ }cot\text{ }qx\] Or, \[tan\text{ }px\text{ }=\text{ }cot\text{ }qx\] or, \[tan\text{ }px\text{ }=\text{ }tan\text{ }\left( \pi /2\text{...
Find the general solutions of the following equations: (vii) tan 2x tan x = 1 (viii) tan mx + cot nx = 0
\[\left( \mathbf{vii} \right)~tan\text{ }2x\text{ }tan\text{ }x\text{ }=\text{ }1\] Or, \[tan\text{ }2x\text{ }tan\text{ }x\text{ }=\text{ }1\] \[tan\text{ }2x\text{ }=\text{ }1/tan\text{ }x\]...
Find the general solutions of the following equations: (v) tan x + cot 2x = 0 (vi) tan 3x = cot x
\[\left( \mathbf{v} \right)~tan\text{ }x\text{ }+\text{ }cot\text{ }2x\text{ }=\text{ }0\] Or, \[tan\text{ }x\text{ }=\text{ }\text{ }cot\text{ }2x\] \[tan\text{ }x\text{ }=\text{ }\text{ }tan\text{...
Find the general solutions of the following equations: (iii) sin 9x = sin x (iv) sin 2x = cos 3x
\[~\left( \mathbf{iii} \right)~sin\text{ }9x\text{ }=\text{ }sin\text{ }x\] Or, \[Sin\text{ }9x\text{ }\text{ }sin\text{ }x\text{ }=\text{ }0\] Using transformation formula, \[Sin\text{ }A\text{...
Find the general solutions of the following equations: (i) sin 2x = √3/2 (ii) cos 3x = 1/2
The general solution of any trigonometric equation is given as: \[sin\text{ }x\text{ }=\text{ }sin\text{ }y,\] or, \[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{n~}}y,\]...
Find the general solutions of the following equations: (v) tan x = -1/√3 (vi) √3 sec x = 2
\[\left( \mathbf{v} \right)~tan\text{ }x\text{ }=\text{ }-1/\surd 3\] Or, \[tan\text{ }x\text{ }=\text{ }-1/\surd 3\] or, \[tan\text{ }x\text{ }=\text{ }tan\text{ }\left( \pi /6 \right)\] \[=\text{...
Find the general solutions of the following equations: (iii) cosec x = – √2 (iv) sec x = √2
\[~\left( \mathbf{iii} \right)~cosec\text{ }x\text{ }=\text{ }\text{ }\surd 2\] Or, \[1/sin\text{ }x\text{ }=\text{ }\text{ }\surd 2\] \[~\left[ as,\text{ }cosec\text{ }x\text{ }=\text{ }1/sin\text{...
Find the general solutions of the following equations: (i) sin x = 1/2 (ii) cos x = – √3/2
The general solution of any trigonometric equation is given as: $$ \[sin\text{ }x\text{ }=\text{ }sin\text{ }y\] Or, \[x\text{ }=\text{ }n\pi \text{ }+\text{ }{{\left( \text{ }1 \right)}^{n~}}y\] ,...