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Question
Evaluate the following without using a table:
`(sec 17°)/("cosec" 73°) + (tan 68°)/(cot 22°)` + cos 44° cosec 46°
Sum
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Solution
Given:
`(sec 17°)/("cosec" 73°) + (tan 68°)/(cot 22°)` + cos 44° cosec 46°
Step 1:
Use complementary-angle identities:
73° = 90° −17° ⇒ cosec 73° = sec 17°
22° = 90° − 68° ⇒ cot 22° = tan 68°
46° = 90° − 44° ⇒ cosec 46° = sec 44°
Step 2:
`(sec 17°)/("cosec" 73°) =1`
`(tan 68°)/(cot 22° = 1)`
cos 44° ⋅ cosec 46° = cos 44° ⋅ sec 44° = 1
= 1 + 1 + 1
= 3
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