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Question
If A = 30° and B = 60°, verify that: `(sin("A" + "B"))/(cos"A" . cos"B")` = tanA + tanB
Solution
A = 30° and B = 60°
L.H.S.
= `(sin("A" + "B"))/(cos"A" . cos"B")`
= `(sin(30° + 60° ))/(cos30° xx cos60°)`
= `(sin"90°)/(cos30° xx cos60°)`
= `(1)/(sqrt(3)/(2) xx (1)/(2)`
= `(4)/sqrt(2)`
R.H.S.
= tanA + tanB
= tan30° + tan60°
= `(1)/sqrt(3) + sqrt(3)`
= `(1 + 3)/sqrt(3)`
= `(4)/sqrt(3)`
⇒ `(sin("A" + "B"))/(cos"A" . cos"B")` = tanA + tanB.
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