Question

f(x)=cos²x+sinx the prove that f(π-x)=f(x)​

Answer 1

Answer:

Step-by-step explanation:

f(x) = cos^2 x + sin x

Now,

       f(π - x) = cos^2 (π - x) + sin (π - x)

                   = cos (π - x) . cos (π - x) + sin (π - x)

                   = (- cos x)(- cos x) + sin x

                   = cos^2 x + sin x

                   = f(x)

Answer 2

Step-by-step explanation:

Given that

$f(x) = \cos( {}^{2} ) x + \sin(x)$

$or \: f(\pi - x) = \cos {}^{2}(\pi - x) + \sin(\pi - x)$

$\: \: \: \: \: \: = ( - \cos \:x) {}^{2} + \sin \: x$

$\: \: \: \: \: \: = \cos {}^{2} x + \sin \: x$

$\: \: \: \: \: \: \: = f(x) \: \: proved$