Evaluate : tan30° sin 30° + cos 60°sin90 tan 60* – 2 tan 45º cos? Oº sin 90°
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To Evaluate:
✰ tan 30° . sin 30° + cos 60° . sin 90° . tan 60° – 2 tan 45º . cos 0º . sin 90°
Solution:
➥ tan 30° . sin 30° + cos 60° . sin 90° . tan 60° – 2 tan 45º . cos 0º . sin 90°
Refer the attachment for the values of standard angles.
Therefore, for standard angles of 0°, 30°, 45°, 60° and 90° of various trigonometric ratios, we have:
➥ 1/√3 × 1/2 + 1/2 × 1 × √3 - 2 × 1 × 1 × 1
➥ 1/√3 × 1/2 + 1/2 × √3 - 2
➥ 1/2√3 + 1/2 × √3 - 2
➥ 1/2√3 + √3/2 - 2
➥ 2 + 2√3 (√3) - 2 ( 2√3 ) ( 2 )/ (2√3) ( 2)
➥ (2 + 6 - 8√3)/4√3
➥ 2(1 + 3 - 4√3)/2 (2√3)
➥ (1 + 3 - 4√3)/2√3
➥ (4 - 4√3)/2√3
➥ 2(2 - 2√3)/2(√3)
➥ (2 - 2√3)/√3
Now, rationalize,
➥ (2 - 2√3 × √3)/(√3 × √3)
➥ (2√3 - 2(√3)²)/(√3)²
➥ (2√3 - 2(√3)²)/(√3)²
Now, square root and square gets cancel,
➥ (2√3 - 2 × 3)/3
➥ (2√3 - 6)/3
Final Answer = (2√3 - 6)/3
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