
Solve the equation:
Answer
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Hint: We need the value of x in such a way that both the sides are equated. If the above example is considered, we need to solve the equation using the standard trigonometric formulae, which are as follows:
Also, we must know the value of sin and cos at particular angles. In this sum we will come across,
Complete step by step answer:
Equation given in the question:
To find: x
We will start solving the sum by multiplying -1 on both sides. We get,
Squaring on both sides, we get
Let us solve the left hand side First, we get,
LHS:
We know that, --1
And ----2
After replacing equation 1 and 2 in the LHS, we get
Now, the original equation becomes,
Taking all the terms to one side and equating them to zero, we get,
Further solving it and by multiplying with -1, we get,
Therefore,
When, ,
I.e. When sin2x=0, we get --3
And When, ,
I.e. When sin2x=1, we get --4
Therefore, from equations 3 and 4.
Note:
Few things should be kept in mind when we come across such questions. Firstly, addition, subtraction, all these methods are to be performed correctly, most of the mistakes happen because of the wrong sign. Secondly, the concepts of trigonometric equations must be well known. Just to be sure about your answer, you can put the value of x in the original equation and compare. And, also that x can take more than 1 value in such sums. Every value obtained is correct.
Also, we must know the value of sin and cos at particular angles. In this sum we will come across,
Complete step by step answer:
Equation given in the question:
To find: x
We will start solving the sum by multiplying -1 on both sides. We get,
Squaring on both sides, we get
Let us solve the left hand side First, we get,
LHS:
We know that,
And
After replacing equation 1 and 2 in the LHS, we get
Now, the original equation becomes,
Taking all the terms to one side and equating them to zero, we get,
Further solving it and by multiplying with -1, we get,
Therefore,
When,
I.e. When sin2x=0, we get
And When,
I.e. When sin2x=1, we get
Therefore,
Note:
Few things should be kept in mind when we come across such questions. Firstly, addition, subtraction, all these methods are to be performed correctly, most of the mistakes happen because of the wrong sign. Secondly, the concepts of trigonometric equations must be well known. Just to be sure about your answer, you can put the value of x in the original equation and compare. And, also that x can take more than 1 value in such sums. Every value obtained is correct.
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