Answer:
PLease
Step-by-step explanation:
Answer:
x = 6
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
x² + (x + 2)² = 10² ← expand parenthesis on left side and simplify
x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )
2x² + 4x - 96 = 0 ( divide through by 2 )
x² + 2x - 48 = 0
(x + 8)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
however, x > 0 , then x = 6
Answer:
cos(π/3)cos(π/5) + sin(π/3)sin(π/5) = cos(2π/15)
Step-by-step explanation:
We will make use of trig identities to solve this. Here are some common trig identities.
Cos (A + B) = cosAcosB – sinAsinB
Cos (A – B) = cosAcosB + sinAsinB
Sin (A + B) = sinAcosB + sinBcosA
Sin (A – B) = sinAcosB – sinBcosA
Given cos(π/3)cos(π/5) + sin(π/3)sin(π/5) if we let A = π/3 and B = π/5, it reduces to
cosAcosB + sinAsinB and we know that
cosAcosB + sinAsinB = cos(A – B). Therefore,
cos(π/3)cos(π/5) + sin(π/3)sin(π/5) = cos(π/3 – π/5) = cos(2π/15)
