Question

If a right ΔABC , right-angled at B, if tan A=1 then verify that 2sin A . cos A = 1

Answer 1

We have,
Tan 𝐴 = 1
⟹`sin A/cosA= 1`
⟹ sin 𝐴 = cos 𝐴
⟹ sin 𝐴 − cos 𝐴 = 0
Squaring both sides, we get
(𝑠𝑖𝑛𝐴 − 𝑐𝑜𝑠𝐴)² = 0
⟹ sin² 𝐴 + cos² 𝐴 − 2 sin 𝐴 . cos 𝐴 = 0 
⟹ 1 − 2 sin 𝐴 . cos 𝐴 = 0
∴ 2 sin 𝐴 . 𝑐𝑜𝑠𝐴 = 1