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प्रश्न
Evaluate the following without using a table:
`(tan 36°)/(cot 54°)` + sin 26° sec 64°
बेरीज
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उत्तर
Given:
`(tan 36°)/(cot 54°)` + sin 26° sec 64°
Step 1:
`(tan 36°)/(cot 54°)`
cot 54° = `1/(tan 54°)`
tan 36° = cot 54° tan A = cot(90° − A)
`(tan 36°)/(cot 54°) + ((tan 36°)/1)/(tan 54°) = tan 36° ⋅ tan 54°`
tan 36° ⋅ tan 54° =
`(tan 36°)/(cot 54°) = 1` ...(i)
Step 2:
sec 64° = `1/(cos 64°)`
cos 64° = sin 26°
sec 64° = `1/(sin 26°)`
sin 26° ⋅ sec 64°
= sin 26° ⋅ `1/(sin 26°)` = 1 ...(ii)
= 1 + 1 ...[Adding (i) & (ii)]
= 2
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