Calculators AI Whiteboard Worksheets & Tests
Book solutions
Algebra Baldor
Go Premium Topics

Prove the trigonometric identity $\left(\sin\left(x\right)+\cos\left(x\right)\right)^2-1=2\sin\left(x\right)\cos\left(x\right)$

Step-by-step Solution

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
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

Solution

Formulas

Videos

Final answer to the problem

true

Step-by-step Solution

How should I solve this problem?

  • Prove from LHS (left-hand side)
  • Prove from RHS (right-hand side)
  • Express everything into Sine and Cosine
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.
1

Starting from the left-hand side (LHS) of the identity

Learn how to solve proving trigonometric identities problems step by step online.

$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2-1$

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)+cos(x))^2-1=2sin(x)cos(x). Starting from the left-hand side (LHS) of the identity. Expand the expression \left(\sin\left(x\right)+\cos\left(x\right)\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Subtract the values 1 and -1.

Final answer to the problem

true

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Help us improve with your feedback!

Function Plot

Plotting: $true$

Similar Problems Solved

Prove the identity

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

Prove the identity

$tan\left(x\right)+cot\left(x\right)=sec\left(x\right)cosec\left(x\right)$

Prove the identity

$\frac{1+\cos2x}{\sin2x}=\cot x$

Prove the identity

$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

Prove the identity

$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Prove the identity

$\tan\left(a\right)+\cot\left(a\right)=\sec\left(a\right)\csc\left(a\right)$

Prove the identity

$\sec x-\sin x\tan x=\cos x$

Main Topic: Proving Trigonometric Identities

To prove a trigonometric identity, you have to show that one side of the equation can be transformed into the other side.

Used Formulas

See formulas (1)

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365 days a year.

Complete step-by-step math solutions. No ads.

Choose between multiple solving methods.

Download solutions in PDF format and keep them forever.

Unlimited practice with our AI whiteboard.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account