find (1-sin^2 0)-cos^2 0
Answers
Answer:
Solving concept. To solve a trig equation, transform it into one, or many, basic trig equations. Solving a trig equation, finally, results in solving various basic trig equations.
There are 4 main basic trig equations:
sin x = a; cos x = a; tan x = a; cot x = a.
Exp. Solve sin 2x - 2sin x = 0
Solution. Transform the equation into 2 basic trig equations:
2sin x.cos x - 2sin x = 0
2sin x(cos x - 1) = 0.
Next, solve the 2 basic equations: sin x = 0, and cos x = 1.
Transformation process.
There are 2 main approaches to solve a trig function F(x).
1. Transform F(x) into a product of many basic trig functions.
Exp. Solve F(x) = cos x + cos 2x + cos 3x = 0.
Solution. Use trig identity to transform (cos x + cos 3x):
F(x) = 2cos 2x.cos x + cos 2x = cos 2x(2cos x + 1 ) = 0.
Next, solve the 2 basic trig equations.
2. Transform a trig equation F(x) that has many trig functions as variable, into a equation that has only one variable. The common variables to be chosen are: cos x, sin x, tan x, and tan (x/2)
Exp Solve
sin
2
x
+
sin
4
x
=
cos
2
x
Solution. Call cos x = t, we get
(
1
−
t
2
)
(
1
+
1
−
t
2
)
=
t
2
.
Next, solve this equation for t.
Note . There are complicated trig equations that require special transformations.
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