prove that : cot x/2 - tan x/2 = 2 cot x
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Answered by
89
cotx/2 - tanx/2
Take x/2 = a for easy notation
= cosa / sina - sina/cosa
= cos²a - sin²a / sin a cosa
Multiply by 2 .
= 2 ( cos2a) / 2sina cosa
= 2cos2a / sin2a
= 2 cot 2a
= 2 cot 2 ( x/2)
= 2 cot x.
Take x/2 = a for easy notation
= cosa / sina - sina/cosa
= cos²a - sin²a / sin a cosa
Multiply by 2 .
= 2 ( cos2a) / 2sina cosa
= 2cos2a / sin2a
= 2 cot 2a
= 2 cot 2 ( x/2)
= 2 cot x.
Answered by
9
Answer:
Step-by-step explanation:
cotx/2 - tanx/2
Take x/2 = a for easy notation
= cosa / sina - sina/cosa
= cos²a - sin²a / sin a cosa
Multiply by 2 .
= 2 ( cos2a) / 2sina cosa
= 2cos2a / sin2a
= 2 cot 2a
= 2 cot 2 ( x/2)
= 2 cot x.
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