Write the expression in terms of sine only help?

sin(x) + cos(x) = sin(x) + sqrt(1 – sin^2(x))

Well the first term is already sin(x), so we just need to express cos(x) in terms of sin(x).

You know the identity sin^2(x) + cos^2(x) = 1, right? Well solving this for cos(x) and substituting it into the original expression gives

sin(x) + ±√[1 – sin^2(x)], which is
sin(x) ± √[1 – sin^2(x)]

(sin(x) + cos(x))^2= sin(x)^2+cos(x)^2+2sin(x)cos(x)
= 1+sin(2x)

Remember that cos(x)^2 + sin(x)^2 = 1, and solve for cos(x).

cos(x)^2 + sin(x)^2 = 1
cos(x)^2 = 1 – sin(x)^2
cos(x) = sqrt(1 – sin(x)^2)

Now just plug that in for cos(x) in the original expression to get sin(x) + sqrt(1 – sin(x)^2).

I am sure you would like it written in terms of sine only without nasty square roots.

asinx + bcosx
sinx + cosx
a = 1, b = 1

ksin(x – α)
k(sinxcosα – cosxsinα)
ksinxcosα – kcosxsinα
kcosαsinx – ksinαcosx
sinx + cosx
kcosα = 1, ksinα = 1

r = √(a² + b²)
r = √(1² + 1²)
r = √2

tana = ksina / kcosa
tana = 1
Sin is positive and cos is positive so a is in quadrant 1
a = atan1
a = 45°

sinx + cos x = √2sin(x + 45)

sin² x +cos² x=1
cos² x=1-sin² x
cosx=(√(1-sin² x))
so I get

sinx+(√(1-sin² x))

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