Evaluate:tan square 30°.sin 30°+cos 60°.sin square 90°.tan square 60°-2.tan 45°.cos square 0°.sin square 90°
Answers
Answer:
Step-by-step explanation:
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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