
How do you find the exact value of using the sum and difference, double angle or half angle formulas?
Answer
471.9k+ views
Hint:In the given question, we have been asked to find the value of sin24 b using any of the formula i.e. sum and difference formula or double angle formula or half angle formula. In order to solve the question, we will use the identity of . We split the , then by using identity we will solve each trigonometric function and by putting into the identity. We will get the required solution.
Formula used:
Difference formula of trigonometry:
Using the trigonometric ratios:
Complete step by step answer:
Using the sum and difference formula:
We have given,
Using the identity; , we obtain
As we know that, using the trigonometric ratio,
Now solving,
Using the identity,
Put the value of
Using the identity,
Simplifying the above, we get
Simplifying further, we obtain
Now solving,
Putting the value of , which we solved above,
Simplifying the above, we get
Putting all the plug-in solved values,
Simplifying the above, we get
Note:In order to solve these types of questions, you should always need to remember the properties of trigonometric and the trigonometric ratios as well. It will make questions easier to solve. It is preferred that while solving these types of questions we should carefully examine the pattern of the given function and then you would apply the formulas according to the pattern observed. As if you directly apply the formula it will create confusion ahead and we will get the wrong answer.
Formula used:
Difference formula of trigonometry:
Using the trigonometric ratios:
Complete step by step answer:
Using the sum and difference formula:
We have given,
Using the identity;
As we know that, using the trigonometric ratio,
Now solving,
Using the identity,
Put the value of
Using the identity,
Simplifying the above, we get
Simplifying further, we obtain
Now solving,
Putting the value of
Simplifying the above, we get
Putting all the plug-in solved values,
Simplifying the above, we get
Note:In order to solve these types of questions, you should always need to remember the properties of trigonometric and the trigonometric ratios as well. It will make questions easier to solve. It is preferred that while solving these types of questions we should carefully examine the pattern of the given function and then you would apply the formulas according to the pattern observed. As if you directly apply the formula it will create confusion ahead and we will get the wrong answer.
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