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Question
Without using trigonometric tables, prove that:
sec 70° sin 20° + cos 20° cosec 70° = 2
Theorem
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Solution
LHS = sec 70° sin 70° + cos 20° cosec 70°
= sec (90° - 20°) sin 20° + cos 20° cosec (90° - 20°)
`= "cosec" 20°. 1/("cosec" 20°)+ 1/(sec 20°) sec 20°`
= 1 + 1
= 2
= RHS
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Chapter 12: Trigonometric Ratios of Some Complemantary Angles - EXERCISE 12 [Page 590]
