Question
Download Solution PDFcos2 35° + cos 55°. sin 35° + \(\frac{\tan34°}{\cot56°}\) = .
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
cos2 35° + cos 55°. sin 35° + \(\frac{\tan34°}{\cot56°}\) = .
Concept used:
1. sin θ = cos (90° - θ)
2. tan θ = cot (90° - θ)
3. sin2 θ + cos2 θ = 1
Calculation:
cos2 35° + cos 55°. sin 35° + \(\frac{\tan34°}{\cot56°}\)
⇒ cos2 35° + cos (90 - 35)°. sin 35° + \(\frac{\tan34°}{\cot(90 - 34)°}\)
⇒ cos2 35° + sin 35°. sin 35° + \(\frac{\tan34°}{\tan34°}\)
⇒ cos2 35° + sin2 35° + 1
⇒ 1 + 1 = 2
∴ The simplified value is 2.
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