Question

Sin2x=1/5 then sinx + cosx =

Answer 1

${( \sin(x) + \cos(x) ) }^{2} = { \sin }^{2}x + { \cos}^{2} x + 2 \sin(x) \cos(x) \\ {( \sin(x) + \cos(x) ) }^{2} = 1 + 2 \sin(x) \cos(x) \\ {( \sin(x) + \cos(x) ) }^{2} = 1 + \sin(2x) \\ {( \sin(x) + \cos(x) ) }^{2} = 1 + \frac{1}{5} = \frac{6}{5} \\ therefore \\ \sin(x) + \cos(x) = \sqrt{ \frac{6}{5} }$

Answer 2

Answer:

Value of   $sin\,x+cos\,x\:is\:\pm\sqrt{\frac{6}{5}}$

Step-by-step explanation:

Given:

sin 2x = 1/5

To find: sin x + cos x

We use the identity,

( a + b )² = a² + b² +2ab

put a = sin and b = cos x

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

( sin x + cos x )² = sin² x + cos² x + 2 sin x cos x

( sin x + cos x )² = 1 + sin 2x   (sin² x + cos² x = 1 and 2 sin x cos x = sin 2x)

( sin x + cos x )² = 1 + 1/5

( sin x + cos x )² = 6/5

sin x + cos x = $\pm\sqrt{\frac{6}{5}}$

Therefore, Value of   $sin\,x+cos\,x\:is\:\pm\sqrt{\frac{6}{5}}$