Question

tan15°+tan30°+tan15° tan30°=1

tan36°+tan9°+tan36° tan9° =1

please help solve these questions​

Answer 1

Answer:

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)