
How do you find the value of using double angle or half angle identity ?
Answer
462.6k+ views
Hint: Here we are given with an angle with its trigonometric function. Actually is a standard angle but we need to convert this angle in the basic angle with the help of double angle or half angle identity. Then we will use the angle with tangent function to find the value of .
Complete step by step solution:
Given that is the angle whose value is to be found.
We know that
So
So we can write
Also we can write
So the identity will be,
We know that
Putting this value in the identity we get,
On calculating the square we get,
On cancelling 2 we get,
Now we will put this value in the identity of
Taking the square,
Cancelling -2,
Now we know that
So putting the value,
Hence, the value of is .
Note: We used half angle identity with double angle form. Also note that if we cannot reach the trigonometric function asked we need to take help of other such trigonometric functions that include or may help to reach the trigonometric function. We can go with the term like we know the value of form for the same trigonometric function.
Complete step by step solution:
Given that
We know that
So
So we can write
Also we can write
So the identity will be,
We know that
Putting this value in the identity we get,
On calculating the square we get,
On cancelling 2 we get,
Now we will put this value in the identity of
Taking the square,
Cancelling -2,
Now we know that
So putting the value,
Hence, the value of
Note: We used half angle identity with double angle form. Also note that if we cannot reach the trigonometric function asked we need to take help of other such trigonometric functions that include or may help to reach the trigonometric function. We can go with the term like we know the value of
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