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Question
Prove the following:
If sin α sin β − cos α cos β + 1 = 0 then prove cot α tan β = −1
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Solution
sin α sin β − cos α cos β + 1 = 0
∴ cos α cos β − sin α sin β = 1
∴ cos (α + β) = 1
∴ α + β = 0 ...[∵ cos 0 = 1]
∴ β = − α
L.H.S. = cot α tan β
= cot α tan (− α)
= − cot α tan α
= − 1
= R.H.S.
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