Question
if
Hint:
In this question, we have given,
. Solve this equation and find the general solution for x.
The correct answer is: ![x equals n pi](data:image/png;base64,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)
Here, we have to find the the general solution for x
Firstly, we have given equation,
![4 sin to the power of 4 space x plus cos to the power of 4 space x equals 1](data:image/png;base64,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)
![equals greater than 4 s i n to the power of 4 x equals 1 minus c o s to the power of 4 x equals left parenthesis 1 minus c o s squared x right parenthesis left parenthesis 1 plus c o s squared x right parenthesis equals s i n squared x left parenthesis 2 minus s i n squared x right parenthesis
equals greater than 4 s i n to the power of 4 x equals s i n squared x left parenthesis 2 minus s i n squared x right parenthesis
equals greater than 4 s i n to the power of 4 x equals 2 s i n squared x minus s i n to the power of 4 x
equals greater than 5 s i n to the power of 4 x equals 2 s i n squared x
equals greater than 5 s i n to the power of 4 x minus 2 s i n squared x equals 0
equals greater than s i n squared x space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket 5 s i n squared x minus 2 right square bracket equals 0](data:image/png;base64,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tbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz4mI3hBMDs8L21vPjxtbz5bPC9tbz48bW4+NTwvbW4+PG1pPnM8L21pPjxtaT5pPC9taT48bXN1cD48bWk+bjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MjwvbW4+PG1vPl08L21vPjxtbz49PC9tbz48bW4+MDwvbW4+PC9tYXRoPsQaEbQAAAAASUVORK5CYII=)
So we can write,
![S i n squared x equals 0 space space a n d space space 5 s i n squared x minus 2 equals 0](data:image/png;base64,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)
x = n π and sin2x =
-2 sin2 x =
1 – 2 sin2 x = ![1 fifth](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAIJJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CoZCDI4WZDQw6BcQfwLibUBcBMQ8lBjIAsTG0IbEDSDWoIYr3YD4ILW8/IMahugA8V1SNa0DYksgZoJiD6ghQaQaFArEt4D4DxC/A+JVQGyKTwMAfKc5il4VJDgAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+NTwvbW4+PC9tZnJhYz48L21hdGg+Xdkl9QAAAABJRU5ErkJggg==)
Cos 2x = ![1 fifth](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAIJJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CoZCDI4WZDQw6BcQfwLibUBcBMQ8lBjIAsTG0IbEDSDWoIYr3YD4ILW8/IMahugA8V1SNa0DYksgZoJiD6ghQaQaFArEt4D4DxC/A+JVQGyKTwMAfKc5il4VJDgAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+NTwvbW4+PC9tZnJhYz48L21hdGg+Xdkl9QAAAABJRU5ErkJggg==)
2x = 2n π ± cos-1 (
)
X = n π ±
cos-1 (
)
Therefore, the correct answer is x = n π and x = n π ±
cos-1 (
). Both options will correct.
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
Related Questions to study
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is
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has
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,then
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,2π and since we also need x≠
,
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) .
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,then
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) .
If ![6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals](data:image/png;base64,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)
If ![6 cos space 2 theta plus 2 cos squared space theta divided by 2 plus 2 sin squared space theta equals 0 comma negative pi less than theta less than pi comma text then end text theta equals](data:image/png;base64,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)
The most general solution of the equations is
The most general solution of the equations is
The general solution of the equation, is
The general solution of the equation, is
The most general solution of cot =
and cosec
= – 2 is :
In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.
The most general solution of cot =
and cosec
= – 2 is :
In this question, we have given cotθ = -√3 and cosecθ = -2. Where θ for both is -π/6 and then write the general solution.