Question

sin 2x + cos x = 0 find the value of x​

Answer 1

Answer:

x = ( 2 n π + 1 ) π / 2

x = n  π + ( - 1 ) ⁿ - π / 6 .

Step-by-step explanation:

sin 2 x + cos x = 0

Using sin 2 x = 2 sin  x cos x

2 sin x cos x + cos x = 0

cos x ( 2 sin x + 1 ) = 0

cos x = 0

or 2 sin x + 1 = 0

2 sin x = - 1

sin x = - 1 / 2

Case 1.

cos x = 0

x = ( 2 n π + 1 ) π / 2

Case 2 .

sin x = - 1 / 2

sin x = sin - π / 6

x = n  π + ( - 1 ) ⁿ - π / 6 .

Thus we get answer .

Answer 2

To find the general solution of the equation sin2∅ + cos∅ = 0

Now,

sin2∅ + cos∅ = 0

→2sin∅cos∅ + cos∅ = 0

→cos∅(2sin∅ + 1) = 0

→2sin∅ + 1 = 0

→sin∅ = -1/2

→sin∅ = -π/6

Also,

sin∅ = (-6π + 5π)/6

→sin∅ = -5π/6

Thus,the principal solutions of the equation are -π/6 and -5π/6

•The general solution would be:

∅ = n(-π/6) + (-1)y