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 x7sin2xsin^2 xsin2x = 8sinxsin xsinxcosxcos xcosx - 1−sin2x1 - sin^2 x1−sin2x 7u2u^2u2 = 8u1−u1 - u1−u - 1 + u2u^2u2 7u^2 = 8u - 8u^2 - 1 + u^27u^2 + 8u - 8u^2 - 1 + u^2 = 07u^2 + 8u - 8u^2 - 1 + u^2 = 00 = 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.
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
7sin2xsin^2 xsin2x = 8sinxsin xsinxcosxcos xcosx - 1−sin2x1 - sin^2 x1−sin2x 7u2u^2u2 = 8u1−u1 - u1−u - 1 + u2u^2u2 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.