7sin^2 x=8 sinx cos x-cos^2x

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вопрос

To solve this equation, we can rewrite it in terms of sine and cosine to simplify:

7sin^2 x = 8 sinx cos x - cos^2 x
7(sin^2 x) = 8(sin x)(cos x) - (1 - sin^2 x)
7(u^2) = 8u(1 - u) - 1 + (u^2)
7u^2 = 8u - 8u^2 - 1 + u^2
7u^2 + 8u - 8u^2 - 1 + u^2 = 0
7u^2 + 8u - 8u^2 - 1 + u^2 = 0
0 = 0

Therefore, the solution to the equation is u=0. Substituting back in, we have sin x = 0. So the solutions to the original equation are x = 0, pi.