Question

(iv) tan 70° = 2 tan 50° + tan 20°​

Answer 1

Step-by-step explanation:

Prerequisites:-

 *  tan(A+B)=tanA+tanB1−tanA.tanB

 *  tanA=cot(90−A)

 *  tanA.cotA=1

We know,

70=50+20

Taking tangent on both sides

= tan70=tan(50+20)

Using Prerequisite (1)

= tan70=tan50+tan201−tan50.tan20

= tan70.(1−tan50.tan20)=tan50+tan20

= tan70−tan70.tan50.tan20=tan50+tan20

= tan70−tan70.tan50.tan(90−70)=tan50+tan20

= tan70−tan70.tan(90−70).tan50=tan50+tan20

Using Prerequisite (2)

= tan70−tan70.cot70.tan50=tan50+tan20

Using Prerequisite (3)

= tan70−1.tan50=tan50+tan20

= tan70=2.tan50+tan20

hope it will help you :)