এর হলে x এর মান কোনটি?
We're given that:
f(x) = sin x + cos x
We need to find the value of x such that:
f(x) + f(-1) = 0
Substituting f(x) and simplifying, we get:
sin x + cos x + sin(-1) + cos(-1) = 0
Using the identity sin(-x) = -sin(x) and cos(-x) = cos(x), we get:
sin x + cos x - sin 1 - cos 1 = 0
Rearranging, we get:
sin x + cos x = sin 1 + cos 1
Now, we can substitute f(x) back into this equation and simplify:
f(x) = sin x + cos x = sin 1 + cos 1
Therefore, we have:
sin x + cos x = sin 1 + cos 1
sin x = sin 1 and cos x = cos 1
Since sin x = sin 1, we have:
x = nπ + (-1)n * 1, where n is any integer.
Similarly, since cos x = cos 1, we have:
x = 2nπ ± 1, where n is any integer.
Therefore, the possible solutions for x are:
x = nπ + (-1)n * 1 or x = 2nπ ± 1, where n is any integer.
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