Question

evalute this. : tan square 30 degree sin 30 degree + Cos 60 degree sin square 90 degree tan square 60 degree minus 2 tan 45 degree cos square 30 degree sin 90 degree​

Answer 1

Given :  tan square 30 degree sin 30 degree + Cos 60 degree sin square 90 degree tan square 60 degree minus 2 tan 45 degree cos square 30 degree sin 90 degree​

Tan²30° Sin30° + Cos60°Sin²90°Tan²60°-2Tan45°Cos²30°Sin90°

To Find : Evaluate

Solution

Tan²30° Sin30° + Cos60°Sin²90°Tan²60°-2Tan45°Cos²30°Sin90°

Tan30°  =  1/√3   =>  Tan²30°  = 1/3

Sin30°  = 1/2

Cos60° = 1/2

Sin90°  = 1  => Sin²90° = 1

Tan²60°  =√3    =>  Tan²60 =  3

Tan45°  = 1

Cos30° = √3/2 => Cos²30° = 3/4

Substitute all values

Tan²30° Sin30° + Cos60°Sin²90°Tan²60°-2Tan45°Cos²30°Sin90°

= (1/3)(1/2) + (1/2)(1)(3) - 2(1)(3/4)(1)

= 1/6  + 1/6  - 3/2

= 2/6  - 3/2

=  2/6  - 9/6

= -7/6

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