| Certified Educator
We have to calculate sin x + sqrt ( 1 - (sin x)^2)
sin x + sqrt ( 1 - (sin x)^2)
=> sin x + sqrt ((cos x)^2)
=> sin x + cos x
This sum can be changed to many other forms but the basic result is sin x + cos x
Therefore the sum = sin x + cos x
To calculate the expression we'll have to transform the sum into a product. The terms of the su are not like trigonometric functions.
We'll re-write the second term: sqrt(1-sin^2x) = sqrt (cos x)^2
sin x + sqrt(1-sin^2x) = sin x + sqrt (cos x)^2
sin x + sqrt(1-sin^2x) = sin x + cos x
We'll express the function cosine, depending on the function sine.
cos x= sin (90-x)
The expression will become:
sin x + cos x = sinx + sin (90-x)
Now we can transform the expression into a product:
sin x + cos x = 2 sin (x+90-x)/2*cos (x-90+x)/2
sin x + cos x = 2 sin 45*cos [-(90-2x)/2]
sin x + cos x = 2* (sqrt2/2)*cos (45-x)
sin x + cos x = sqrt 2*(cos 45*cos x + sin 45*sin x)
Access hundreds of thousands of answers with a free trial.
- Calculate the expression sin^-1(sin(5pi/3))+tan^-1(tan(2pi/3))?
- 1 educator answer
- Prove the following identity: (1+ sin x + cos x) / (1+ sin x - cos x) = cot x/2
- 1 educator answer
- Prove that sin^4 x+cos^4 x+(sin^2 2x)/2=1
- 1 educator answer
- finding an anglewhat is the x angle if 2sin2x+square root 2=0?
- 1 educator answer
- What is x if (1+cos2x)/2=sin(-2x)?
- 1 educator answer
- How do we derive the expansion for sin 3x?
- 1 educator answer
- Prove the following identity: cos x + cos 2x + cos 3x = cos 2x(1 + 2cos x)
- 1 educator answer
- What is the angle x if the identity sin2x-(cos 2x)/2 -1/2=cosx-2cosx*tanx?
- 1 educator answer
- how to evaluate cos13pi/6 and sin37pi/4?
- 1 educator answer
- trigonometryGiven that sina + sinb =1 and cosa + cosb = 1/2 calculate cos(a-b) .
- 1 educator answer
