Question

tan20°+2tan50°=tan70°​

Answer 1

Answer:

tan70°=tan(50°+20°)  

Using formula

tan(A+B)=tanA+tanB1−tanA×tanB

tan70°=tan50°+tan20°1−tan50°×tan20°

tan70°−tan70°tan50°tan20°=tan50°+tan20°

tan70°=tan20°+tan50°+tan70°tan50°tan20°

tan70°=tan20°+tan50°(1+tan70°×tan20°)

tan70°=tan20°+tan50°(1+tan(90°−20°)×tan20°)

tan70°=tan20°+tan50°(1+cot20°×tan20°)

tan70°=tan20°+tan50°(1+tan20°tan20°)

Since (cotθ=1tanθ)

tan70°=tan20°+tan50°(1+1)

tan70°=tan20°+2tan50°

Hence proved

Answer 2

Step-by-step explanation:

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