Evaluate sin15 × cos75 + cos15 × sin75 / tan15 × tan30 × tan35 ×tan55 × tan85
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sin 15 × cos 75 + cos 15 × sin 75 / tan15 × tan 30 × tan35 × tan55 × tan 85
= sin 15 × cos(90-15) + cos(90-75) × sin 75 / tan30 × tan35 × cot35 × tan15 × cot15
= sin15 × sin15 + sin75 + sin75 / 1/√3 ×1
= sin^2 15 + sin^2 75 × √3
= sin^2 15 + cos^2 15 × √3
= 1 ×√3
= √3
I hope this helps with your friend.
= sin 15 × cos(90-15) + cos(90-75) × sin 75 / tan30 × tan35 × cot35 × tan15 × cot15
= sin15 × sin15 + sin75 + sin75 / 1/√3 ×1
= sin^2 15 + sin^2 75 × √3
= sin^2 15 + cos^2 15 × √3
= 1 ×√3
= √3
I hope this helps with your friend.
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