Question

how to prove that : tan 15°+tan 30°+tan15°.tan30° = 1 ??? can anyone please help here?

Answer 1

As we know tan(A +B) = (tanA +tanB)/(1 -tanA.tanB)
putting, A= 30° and B = 15°,
tan(30° +15°)=(tan30° +tan15°)/(1 - tan30°.tan15°)
⇒tan(45°)=(tan30° +tan15°)/(1 - tan30°.tan15°)
⇒1=(tan30° +tan15°)/(1 - tan30°.tan15°)
⇒(1 - tan30°.tan15°) =(tan30° +tan15°)
⇒(tan30° +tan15° +tan30°.tan15°) =1  (proved)

Answer 2

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