cosh(2x)-10cosh(x)+13=0

Solution

cosh (2 x) - 10 cosh (x) + 13 = 0

x = ln (0.17157 \dots), x = ln (0.26794 \dots), x = ln (3.73205 \dots), x = ln (5.82842 \dots)

Solution steps

cosh (2 x) - 10 cosh (x) + 13 = 0

Rewrite using trig identities

\frac{e ^{2 x} + e ^{- 2 x}}{2} - 10 \cdot \frac{e ^{x} + e ^{- x}}{2} + 13 = 0

\frac{e ^{2 x} + e ^{- 2 x}}{2} - 10 \cdot \frac{e ^{x} + e ^{- x}}{2} + 13 = 0 : x = ln (0.17157 \dots), x = ln (0.26794 \dots), x = ln (3.73205 \dots), x = ln (5.82842 \dots)

x = ln (0.17157 \dots), x = ln (0.26794 \dots), x = ln (3.73205 \dots), x = ln (5.82842 \dots)

3 sin (x) - sin (2 x) = 0

7 cos^{2} (x) + 14 cos (x) + 7 = 0

θ, 2 sin (θ) = 2 cos (2 θ)

sec (θ) + 4 = 4 sec (θ)

sin (2 x) - 4 \cdot cos (x) = 0