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Question
यदि `tanA = (1 − cosB)/sinB`, तो tan2A = ______.
Fill in the Blanks
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Solution
विस्तृत करने पर, tan A = `(1 - cos "B")/sin"B"`
ज्ञात है कि, tan2A = `(2tan"A")/(1 - tan^2"A")`
∴ tan2A = `(2((1 - cos "B")/sin"B"))/(1 - ((1 - cos "B")/sin"B")^2`
⇒ tan2A = `(2((2sin^2 "B"/2)/(2sin "B"/2 cos "B"/2)))/(1 - ((2sin^2 "B"/2)/(2sin "B"/2 cos "B"/2))^2`
= `(2tan B/2)/(1 - tan^2 B/2)`
= tanB
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