Question
Download Solution PDFThe value of tan 16° + 2 + tan 16° cot 61° + [4(sin 41° cos 41°)/cos 8°] + cot 61° is -
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tan 16° + 2 + tan 16° cot 61° + [4(sin 41° cos 41°)/cos 8°] + cot 61°
Formula Used:
- When, x+ y = 45° ⇒ tan x + tan y + tan x tan y = 1
- sin(90° - θ) = cos θ
- cot(90° - θ) = tan θ
- 2sin θ cos θ = sin 2θ
Calculation:
tan 16° + 2 + tan 16° cot 61° + [4(sin 41° cos 41°)/cos 8°] + cot 61°
⇒ tan 16° + 2 + tan 16° cot(90° - 29°) + [2(2 sin 41° cos 41°)/cos 8°] + cot(90° - 29°)
By using the formula discussed above
⇒ tan 16° + 2 + tan 16° tan 29° + 2(sin 82°)/cos 8° + tan 29°
⇒ (tan 16° + tan 29° + tan 16° tan 29°) + 2 + 2 sin(90°- 8°)/cos 8°
Since, 16° + 29° = 45° then, tan 16° + tan 29° + tan 16° tan 29° = 1
⇒ 1 + 2 + 2 cos 8°/cos 8°
⇒ 1 + 2 + 2
⇒ 5
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