Докажите тождество:

1) cos^4t-sin^4t=cos2t

2) cos^4t+sin^4t=1 - (1/2) sin^2 * 2t

Question

Алгебра

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14 октября, 21:50

Докажите тождество:

1) cos^4t-sin^4t=cos2t

2) cos^4t+sin^4t=1 - (1/2) sin^2 * 2t

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Рима · Answer 1

1 + (cos^4t+sin^2tcos^2t) / sin^2t=1/sin^2t 1 + cos^2t (cos^2t+sin^2t) / sin^2t=1/sin^2t 1 + cos^2t/sin^2t=1/sin^2t (cos^2t+sin^2t) / sin^2t = 1/sin^2t 1/sin^2t = 1/sin^2t 1=1 тождество доказано.

Докажите тождество:1) cos^4t-sin^4t=cos2t2) cos^4t+sin^4t=1 - (1/2) sin^2 * 2t

Докажите тождество:

1) cos^4t-sin^4t=cos2t

2) cos^4t+sin^4t=1 - (1/2) sin^2 * 2t