Solve (sin x + cos x)(sin x + cos x)

Solve (sin x + cos x)(sin x + cos x)

Question
Solve \((\sin x + \cos x)(\sin x + \cos x)\)

Answers (1)

2021-03-09
Use Distributive Property of FOIL method to obtain:
\(\sin^{2}x+2\sin x\cos x+\cos^{2}x\)
Use the identity: \(\sin^{2}x+\cos^{2}x=1\)
\(=1+2\sin x\cos x\)
Use the double-angle identity: \(\sin^{2}x=2\sin x\cos x\)
\(=1+\sin2x\)
0

Relevant Questions

asked 2020-11-10
Solve \(\frac{\csc x(sin^{2}x+cos^{2}x\tan x)}{\sin x+\cos x}\)
asked 2021-03-04
Solve \(\frac{(\sin \theta+\cos \theta)}{\cos \theta}+\frac{(\sin \theta-\cos \theta)}{\cos \theta}\)
asked 2020-10-18
Solve \cos 30° \cos 35° - \sin 30° \sin 35°
asked 2021-02-21
Multiply and simplify: \(\frac{(\sin \theta+\cos \theta)(\sin \theta+\cos \theta)-1}{\sin \theta \cos \theta}\)
asked 2021-01-17
Solve \(\frac{(1-\sin^{2}x)}{(csc^{2}x-1)}\)
asked 2021-02-13
What is the solution of \(\cos2x - \cos x = 0\ \text{in the interval}\ [0, 2\pi )\) ?
asked 2020-10-25
Evaluate the following.
\(\displaystyle\int{\frac{{{{\cos}^{{5}}{\left({3}{z}\right)}}{\left.{d}{z}\right.}}}{{{{\sin}^{{2}}{\left({3}{z}\right)}}}}}\)
asked 2021-03-11
For a Science fair project, a group of students tested different Materials used to construct kites. The instructor gave to the group an instrument that accurately measures the angle of elevation. In one of the tests, the angle of elevation was 63.4° with 670 ft of string out. Assuming the string was taut, how high was the kite?
asked 2020-10-26
Solve the equation
\(\displaystyle{\sin{{\left({x}°-{20}°\right)}}}={\cos{{42}}}°\) for x, where 0 < x < 90
asked 2021-01-17
Solve the equation \(\csc x - \sin x = \cot x \cos x\)
...