Обчислить значение выраза tg²15°+tg²75°=

tg²15° + tg²75° = (tg15° + tg75°)² - 2tg15°tg75° = [tg75° = ctg15°] = (tg15° + tg75°)² - 2tg15°ctg15°= [tg15°ctg15° = 1] = (tg15° + tg75°)² - 2

найдем tg15° + tg75° = sin(15° + 75°)/(cos15°cos75°) = [cos75° = sin15°] = sin90°/(cos15°sin15°) = [sin15°cos15° = 0,5sin30°] = 1/(0,5sin30°) =

= [sin30° = 0,5] = 1/(0,5*0,5) = 4

tg²15° + tg²75° = (tg15° + tg75°)² - 2 = 4² - 2 = 14

ответ: 14