Firstly, express tan θ as sin θ/cos θ, then use the Pythagorean identity to find sin2 θ and cos2 θ. Solve for sin2 θ and cos2 θ using the given tan θ. The final result is sin2 θ - cos2 θ = -4/5.
If 3 tan θ = 1, then to find the value of sin2 θ − cos2 θ, you first need to express tan θ in terms of sine and cosine, which gives you tan θ = sin θ/cos θ. Now, since 3 tan θ = 3 (sin θ/cos θ) = 1, then sin θ/cos θ = 1/3.
To find sin2 θ and cos2 θ, you can use the Pythagorean identity, 1 = sin2 θ + cos2 θ. We already have a value for tan θ, which allows us to solve for sin θ and cos θ individually. From sin θ/cos θ = 1/3, you can cross multiply to find that sin θ = cos θ / 3. Now, if you square both sides of the equation, you'll get sin2 θ = (cos θ)2 / 9.
Using the Pythagorean identity, let cos2 θ = x, then sin2 θ = x/9, and according to the identity, x + x/9 = 1, or 10x/9 = 1, which implies x = 9/10. Therefore, sin2 θ = (9/10)/9 = 1/10 and cos2 θ = 9/10. Finally, sin2 θ - cos2 θ = 1/10 - 9/10 = -8/10 or -4/5.
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Answer:
sin2θ - cos2θ = 2sin² θ
Step-by-step explanation:
hello :
tan θ = 1 means : sinθ /cosθ so : sinθ =cosθ
sin2θ = 2sin θ cosθ =2sin² θ
cos2θ = cos²θ - sin²θ = sin²θ - sin²θ =0
sin2θ - cos2θ = 2sin² θ
Answer:
First fund: $4000
second account: $2000
Step-by-step explanation:
invest x for first fund (A) and y for second fund (B)
interest for A: x * 0.05
interest for B: y * 0.09
0.05 x + 0.09 y = 380 ....(1)
x + y = 6000 ..... (2)
y = 6000 - x ....substitute y in (1)
0.05 x + 0.09 (6000 - x) = 380
0.05x + 540 - 0.09x = 380
0.04 x = 160
x = 4000
y = 6000 -4000 = 2000
check: 4000 x 0.05 + 2000 x 0.09 = 200 + 180 = 380
The slope m of a straight line passing through points (x₁,x₂) and (y₁,y₂) can be calculated like this:
m = change in y-value / change in x-value
m = (y₂ - y₁) / (x₂ - x₁)
We are given the points as (7,r) and (4,6) and slope m=0 . Substituting these:
⇒m = 6 - r / 4 - 7
⇒0 = 6 - r / -3
∴ r = 6
The resultant of the given equation will be : y = 21
Given,
2/3y+y-4=31
Here,
First add the terms having same variable.
Add 2/3 y and y
2/3 y + y
= 5y/3
Now take -4 from LHS to RHS ,
5y/3 = 35
y = 7* 3
y = 21
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