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प्रश्न
Evaluate the following without using a table:
`2 (tan 32°)/(cot 58°) + (sec 46°)/("cosec" 44°)`
बेरीज
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उत्तर
Given:
`2 (tan 32°)/(cot 58°) + (sec 46°)/("cosec" 44°)`
Step 1:
cot(90° − θ) = tan θ and cosec(90° − θ) = sec θ
Since 58° = 90° − 32°
cot 58° = tan 32°
`(tan 32°)/(cot 58°)` = 1
so 2 × 1 = 2 ...[(i)]
Step 2:
44° = 90° − 46°, cosec 44° = sec 46°
`(sec 46°)/("cosec" 44°)` = 1 ...[(ii)]
= 2 + 1 ...[Adding (i) & (ii)]
= 3
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