Tg23*tg293+sin52*sin128-sin322*sin142

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The calculation for Tg23tg293+sin52sin128-sin322*sin142 is as follows:

tg(23) tg(293) + sin(52) sin(128) - sin(322) * sin(142)

Using trigonometric identity:

tg(a) * tg(b) = 1 - cos(a - b) / cos(a + b)

sin(a) sin(b) = 1/2 [cos(a - b) - cos(a + b)]

The calculation can be simplified using the trigonometric identities:

1 - cos(23-293) / cos(23+293) + 1/2 [cos(52-128) - cos(52+128)] - 1/2 [cos(322-142) - cos(322+142)]

= 1 - cos(-270) / cos(316) + 1/2 [cos(-76) - cos(180)] - 1/2 [cos(180) - cos(464)]

= 1 - cos(270) / cos(316) + 1/2 [cos(76) + 1] - 1/2 [-1 - cos(464)]

= 1 - 0 / cos(316) + 1/2 [0.245 + 1] - 1/2 [-1 - 0.807]

= 1 / cos(316) + 1/2 1.245 - 1/2 -1.807

= 1 / cos(316) + 0.6225 + 0.9035

= 1 / -0.545 + 0.6225 + 0.9035

= -1.834 + 0.6225 + 0.9035

= -0.308

Therefore, Tg23tg293+sin52sin128-sin322*sin142 is approximately equal to -0.308.