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Question
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
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Solution
LHS = `cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°)`
= `cos^2 26° + cos (90° - 26°) sin 26° + (tan 36°)/(cot (90° - 54°)`
= `cos^2 26° + sin 26°. sin 26° + (tan 36°)/(tan 36°)`
= cos2 26° + sin2 26 + 1 ....( cos2 θ + sin2 θ = 1)
= 1 + 1 = 2
= RHS
Hence proved.
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