sin15 cos75 plus sin75 cos15 divided by tan5tan30tan35tan55tan85
Answers
Answer:
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Answer:
√3
Step-by-step explanation:
Numerator:
sin15°cos°75 + sin75°cos15° = sin(90-15)cos75 + sin75°cos(90-15)
*Complementary angles—sin(90-ϑ) = cosϑ*
= cos75°cos75° + sin75°sin75°
= cos²75° + sin²75°
= 1
*Identity—sin²ϑ - cos²ϑ = 1*
Denominator:
tan5°tan30°tan35°tan55°tan85° = tan(90-5) tan30° tan(90-35) tan 55° tan85°
= cot85° tan 30° cot55° tan55° tan85°
= tan30°
= 1/√3
sin15°cos°75 + sin75°cos15 / tan5°tan30°tan35°tan55°tan85° = 1 ÷ 1/√3
= 1 × √3
= √3
Hope it helps you:)