Question

Solve the equation sin4 x + cos4 x = 7/2 sin x cos x

Answer 1

Step-by-step explanation:

We transform the expression sin^4 x + cos^4 x isolating a perfect square:

sin^4 x + cos^4 x = sin^4 x + 2 sin^2 x cos^2 x + cos^4 x – 2 sin^2 x cos^2 x

= (sin^2 x + cos^2 x)2 – 2 sin^2 x cos^2 x, which gives

sin^4 x + cos^4 x = 1 – 1/2 sin^2 2x. … (1)

Using (1), the given equation becomes

1 – 1/2 sin^2 2x = 7/4 sin^2x.

2 sin2^ 2x + 7sin 2x – 4 = 0

⇒ (2 sin 2x – 1) (sin^2x + 4) = 0

So, either 2 sin 2x – 1 = 0 or sin 2x + 4 = 0        

This gives 2 x = nπ + (–1)n π/6          where n = 0, ±1, ±2… …                    

or sin 2x + 4 = 0 gives no solution as –4 does not belong to range of sin 2x.

The solution of equation is x = (nπ)/2 + (–1)n π/12, where n = 0, ± 1, ± 2

thanks.....

Answer 2

Answer:

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Step-by-step explanation:

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