Question

if sin2x=1/5,sinx +cosx is

Answer 1

sinx + cosx /10sinxcox

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  

( sin x + cos x )² = 1 + 1/5

( sin x + cos x )² = 6/5

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

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