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