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Simplify the trigonometric expression $\sin\left(a\right)^4-\cos\left(a\right)^4+\cos\left(a\right)^2$

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Solution

Formulas

Videos

Proof the identity sin(x)^2 = 1 - cos(x)^2

https://www.youtube.com/watch?v=g7eVgtmQ7Dk

Pre-Calculus - How to simplify a trigonometric expression by squaring a binomial (sin(x)+cos(x))^2

https://www.youtube.com/watch?v=e5IczuZxvVI

Tutorial - Simplify a rational trigonometric expression 24, ((sinx)^2 - (cosx)^2) / (1 - 2(cosx)^2)

https://www.youtube.com/watch?v=taFMJ3iNVhM

Tutorial - Simplify a trigonometric expression by factoring ex 26, 2(cosx)^2 + cosx - 3

https://www.youtube.com/watch?v=X35--yiv4Ms

Pre-Calculus - Factor and use fundamental identities to simplify, ((cosx)^2 -4)/(cosx - 2)

https://www.youtube.com/watch?v=D0UPURfyahI

Pre-Calculus - Simplifying an expression using the sum formula for sine sin(3π/2+θ)

https://www.youtube.com/watch?v=_6Lrq-H147M

Function Plot

Plotting: $\sin\left(a\right)^2$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Similar Problems Solved

$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2$

$1+cot^2x$

$tan\left(x\right)csc\left(x\right)$

$\tan\left(x\right)\csc\left(x\right)$

$\frac{2+\tan^2\left(x\right)}{\sec^2\left(x\right)}-1$

$csc^2x-1$

$\frac{2+tan^2x}{sec^2x}-1$

Main Topic: Simplify Trigonometric Expressions

Simplification of trigonometric expressions consists of rewriting an expression with trigonometric functions in a simpler form. To perform this task, we usually use the most common trigonometric identities, and some algebra.

Used Formulas

See formulas (1)

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