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Question

f (x) = \sin x + \cos x

এর

f (x) + f (- 1) = 0

হলে x এর মান কোনটি?

\frac{- π}{2}

\frac{π}{2}

\frac{π}{\sqrt{2}}

ANSWER : 2

Descrption

We're given that:f(x) = sin x + cos xWe need to find the value of x such that:f(x) + f(-1) = 0Substituting f(x) and simplifying, we get:sin x + cos x + sin(-1) + cos(-1) = 0Using the identity sin(-x) = -sin(x) and cos(-x) = cos(x), we get:sin x + cos x - sin 1 - cos 1 = 0Rearranging, we get:sin x + cos x = sin 1 + cos 1Now, we can substitute f(x) back into this equation and simplify:f(x) = sin x + cos x = sin 1 + cos 1Therefore, we have:sin x + cos x = sin 1 + cos 1sin x = sin 1 and cos x = cos 1Since 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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